diff --git a/sage/tnfs/param/testvector_other_sparseseed.py b/sage/tnfs/param/testvector_other_sparseseed.py
index 9488d4138a7537158522236a0af98419d3edef85..3bac28db3a4fb2e593ce100aea348d19559f1027 100644
--- a/sage/tnfs/param/testvector_other_sparseseed.py
+++ b/sage/tnfs/param/testvector_other_sparseseed.py
@@ -294,6 +294,31 @@ test_vector_fst66_k22 = [
     {'u':-0x925d3, 'u_mod_11':4, 'b': 1, 'pnbits':536,'rnbits':384, 'deg_h_S':None,'cost_S':None, 'label':"u=-2^19-2^16-2^13-2^11+2^9+2^6-2^4-2^2+1 Hw2NAF=9"},#36
 ]
 
+# BLS15, choose u = 1, 7 mod 15 to ensure p = 1 mod 15 for easier towering, that is, u = 1, 2 mod 5 (u = 1 mod 3 by design)
+# BLS15 curves with sparse seed u = [1, 4] mod 6 of 48--49 bits Hw2naf 5 and s.t. r has 380 to 384 bits
+test_vector_sparse_bls15 = [
+    {'u': 0xa7ffffffffec, 'u_mod_5':3, 'b': 2, 'pnbits':568, 'rnbits':380, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"+2^47+2^45+2^43-2^4-2^2 Hw2naf 5"},
+    {'u': 0xffffffbffffe, 'u_mod_5':0, 'b': 2, 'pnbits':575, 'rnbits':384, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"+2^48-2^22-2 Hw2naf 3"},
+    {'u':-0xffffc0000050, 'u_mod_5':3, 'b':-2, 'pnbits':575, 'rnbits':384, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"-2^48+2^30-2^6-2^4 Hw2naf 4"},
+    {'u':-0xffffc3fffffe, 'u_mod_5':1, 'b':16, 'pnbits':575, 'rnbits':384, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"-2^48+2^30-2^26+2 Hw2naf 4"},
+    {'u':-0xfffe00fc0000, 'u_mod_5':4, 'b':-2, 'pnbits':575, 'rnbits':384, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"-2^48+2^33-2^24+2^18 Hw2naf 4"},
+    {'u':-0xff3fe0000000, 'u_mod_5':3, 'b':-2, 'pnbits':575, 'rnbits':384, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"-2^48+2^40-2^38+2^29 Hw2naf 4"},
+    {'u': 0xf7fffffff804, 'u_mod_5':4, 'b': 2, 'pnbits':574, 'rnbits':384, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"+2^48-2^43-2^11+2^2 Hw2naf 4"},
+    {'u':-0xbffff8001000, 'u_mod_5':0, 'b':-2, 'pnbits':570, 'rnbits':381, 'cost_S':160, 'deg_h_S':15, 'cost_C':177, 'deg_h_C':3, 'label':"-2^48+2^46+2^27-2^12 Hw2naf 4"},
+    # BLS15 curves with sparse seed u = [1, 4] mod 6 of 64--65 bits Hw2naf 5 and s.t. p has 760 to 768 bits, r > 512 bits removed
+    {'u': -0xffffffffdfffe080, 'u_mod_5':0, 'b':-2, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"-2^64+2^29+2^13-2^7 Hw2naf 4"},
+    {'u': -0xffffffff00000380, 'u_mod_5':4, 'b':-2, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"-2^64+2^32-2^10+2^7 Hw2naf 4"},
+    {'u':  0xfffffffe00fff800, 'u_mod_5':2, 'b':-2, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"+2^64-2^33+2^24-2^11 Hw2naf 4"},
+    {'u': -0xffffbfffff800100, 'u_mod_5':0, 'b':-2, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"-2^64+2^46+2^23-2^8 Hw2naf 4"},
+    {'u':  0xffff7fe000040000, 'u_mod_5':0, 'b':-2, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"+2^64-2^47-2^37+2^18 Hw2naf 4"},
+    {'u': -0xfff7f80000000800, 'u_mod_5':2, 'b':-2, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"-2^64+2^51+2^43-2^11 Hw2naf 4"},
+    {'u': -0xfff0000038000000, 'u_mod_5':4, 'b':-2, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"-2^64+2^52-2^30+2^27 Hw2naf 4"},
+    {'u': -0xfbffffffffffffde, 'u_mod_5':2, 'b':14, 'pnbits':767, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"-2^64+2^58+2^5+2 Hw2naf 4"},
+    {'u': -0xf800000048000000, 'u_mod_5':0, 'b':-2, 'pnbits':766, 'rnbits':512, 'cost_S':178, 'deg_h_S':15, 'cost_C':200, 'deg_h_C':3, 'label':"-2^64+2^59-2^30-2^27 Hw2naf 4"},
+    # BLS15 curves with sparse seed u = [1, 4] mod 6 of 75--76 bits Hw2naf 4 and s.t. p has 890 to 896 bits
+    {'u':-0x4ffbffff80000000000, 'u_mod_5':2, 'b':-2, 'pnbits':891, 'rnbits':595, 'cost_S':190, 'deg_h_S':15, 'cost_C':213, 'deg_h_C':3, 'label':"-2^74-2^72+2^62+2^43 Hw2naf 4"},
+    {'u': 0x600000007fc00000000, 'u_mod_5':0, 'b':-2, 'pnbits':894, 'rnbits':597, 'cost_S':190, 'deg_h_S':15, 'cost_C':213, 'deg_h_C':3, 'label':"+2^75-2^73+2^43-2^34 Hw2naf 4"},
+]
 
 # BLS21 curves with sparse seed u = [1, 4] mod 6 of 33--33 bits Hw2naf 5 and s.t. r has 384 to 384 bits
 # u % 7 == 1 allows to have p = 1 mod 7 as (px-1).roots(GF(7)) gives root (1).