Cremona's table of elliptic curves

86688 = 2⁵ · 3² · 7 · 43

Class	r	Atkin-Lehner	Eigenvalues
86688a (2 curves)	1	2+ 3+ 7+ 43+	2+ 3+  4 7+  0 -2 -6 -4
Curve Equation t Generators 86688a1 [0,0,0,-2673,-55620] 2 [3720:39970:27] 86688a2 [0,0,0,-43308,-3468960] 2 [6541230:-13727411:27000]
86688b (1 curve)	0	2+ 3+ 7+ 43-	2+ 3+  1 7+ -2 -5  5  1
Curve Equation t 86688b1 [0,0,0,-2187,34722] 1
86688c (1 curve)	0	2+ 3+ 7+ 43-	2+ 3+ -1 7+  6  5  7  7
Curve Equation t 86688c1 [0,0,0,-355563,81458946] 1
86688d (2 curves)	0	2+ 3+ 7+ 43-	2+ 3+ -2 7+  4 -2  2 -8
Curve Equation t 86688d1 [0,0,0,-11961,-501660] 2 86688d2 [0,0,0,-6156,-989280] 2
86688e (1 curve)	0	2+ 3+ 7- 43+	2+ 3+  1 7-  6  5 -7 -7
Curve Equation t 86688e1 [0,0,0,-39507,3016998] 1
86688f (1 curve)	2	2+ 3+ 7- 43+	2+ 3+ -1 7- -2 -5 -5 -1
Curve Equation t Generators 86688f1 [0,0,0,-243,1286] 1 [-2:42:1]&[5:14:1]
86688g (2 curves)	0	2+ 3+ 7- 43+	2+ 3+  2 7-  4 -2 -2  8
Curve Equation t 86688g1 [0,0,0,-1329,-18580] 2 86688g2 [0,0,0,-684,-36640] 2
86688h (2 curves)	1	2+ 3+ 7- 43-	2+ 3+ -4 7-  0 -2  6  4
Curve Equation t Generators 86688h1 [0,0,0,-297,-2060] 2 [27:98:1] 86688h2 [0,0,0,-4812,-128480] 2 [156:1708:1]
86688i (4 curves)	0	2+ 3- 7+ 43+	2+ 3-  2 7+  0 -2 -2 -4
Curve Equation t 86688i1 [0,0,0,-6429,-187220] 4 86688i2 [0,0,0,5181,-788618] 2 86688i3 [0,0,0,-19659,831490] 2 86688i4 [0,0,0,-101244,-12399392] 2
86688j (1 curve)	2	2+ 3- 7+ 43+	2+ 3- -2 7+  3 -3 -3 -4
Curve Equation t Generators 86688j1 [0,0,0,4344,1679344] 1 [36:-1372:1]&[20:1332:1]
86688k (2 curves)	1	2+ 3- 7+ 43-	2+ 3-  0 7+  0 -6 -6  4
Curve Equation t Generators 86688k1 [0,0,0,-45,-1188] 2 [184:2494:1] 86688k2 [0,0,0,-1980,-33696] 2 [-27:9:1]
86688l (1 curve)	1	2+ 3- 7+ 43-	2+ 3-  2 7+  1 -3  5 -8
Curve Equation t Generators 86688l1 [0,0,0,81096,9882448] 1 [-31:2709:1]
86688m (2 curves)	1	2+ 3- 7+ 43-	2+ 3- -2 7+  6  2  2  0
Curve Equation t Generators 86688m1 [0,0,0,-381,-2000] 2 [-7:18:1] 86688m2 [0,0,0,-2316,41344] 2 [-10:252:1]
86688n (2 curves)	1	2+ 3- 7+ 43-	2+ 3- -4 7+ -2  6  2  4
Curve Equation t Generators 86688n1 [0,0,0,-95637,90876760] 2 [-133:10062:1] 86688n2 [0,0,0,-3673452,2695526080] 2 [942:8428:1]
86688o (1 curve)	1	2+ 3- 7- 43+	2+ 3-  1 7-  6  1  1  7
Curve Equation t Generators 86688o1 [0,0,0,-53787,-4801358] 1 [-296200860478:530249292:2212245127]
86688p (1 curve)	1	2+ 3- 7- 43+	2+ 3- -1 7- -2  7  7  5
Curve Equation t Generators 86688p1 [0,0,0,-81003,-8859454] 1 [-1342:729:8]
86688q (1 curve)	1	2+ 3- 7- 43+	2+ 3-  2 7-  1 -2  4  5
Curve Equation t Generators 86688q1 [0,0,0,-579,-6442] 1 [29:34:1]
86688r (1 curve)	1	2+ 3- 7- 43+	2+ 3-  2 7- -1 -3  5  8
Curve Equation t Generators 86688r1 [0,0,0,81096,-9882448] 1 [3316:191628:1]
86688s (4 curves)	1	2+ 3- 7- 43+	2+ 3-  2 7-  4 -2 -2 -4
Curve Equation t Generators 86688s1 [0,0,0,-1505829,702400340] 4 [-815:37260:1] 86688s2 [0,0,0,-178419,1897334822] 2 [-461394:30554810:729] 86688s3 [0,0,0,-2916444,-822192352] 2 [24181:3750705:1] 86688s4 [0,0,0,-24010059,45283279970] 2 [25139646990:-4253569030:8869743]
86688t (2 curves)	1	2+ 3- 7- 43+	2+ 3-  2 7-  4  4 -2  2
Curve Equation t Generators 86688t1 [0,0,0,771,-772] 2 [19:144:1] 86688t2 [0,0,0,-3099,-6190] 2 [62:200:1]
86688u (4 curves)	1	2+ 3- 7- 43+	2+ 3- -2 7-  0 -2 -2  4
Curve Equation t Generators 86688u1 [0,0,0,-5421,153340] 4 [-31:540:1] 86688u2 [0,0,0,-3531,261826] 2 [-206:4635:8] 86688u3 [0,0,0,-7356,34144] 2 [-4:252:1] 86688u4 [0,0,0,-86691,9824470] 2 [270:2470:1]
86688v (1 curve)	1	2+ 3- 7- 43+	2+ 3- -2 7-  3  5 -7 -4
Curve Equation t Generators 86688v1 [0,0,0,-936,-11664] 1 [36:36:1]
86688w (2 curves)	1	2+ 3- 7- 43+	2+ 3- -2 7- -6  2  2  0
Curve Equation t Generators 86688w1 [0,0,0,-381,2000] 2 [25:90:1] 86688w2 [0,0,0,-2316,-41344] 2 [-26:36:1]
86688x (2 curves)	1	2+ 3- 7- 43+	2+ 3- -4 7-  2  6  2 -4
Curve Equation t Generators 86688x1 [0,0,0,-95637,-90876760] 2 [809:19006:1] 86688x2 [0,0,0,-3673452,-2695526080] 2 [-1138:3332:1]
86688y (1 curve)	0	2+ 3- 7- 43-	2+ 3- -1 7-  0  1  3  1
Curve Equation t 86688y1 [0,0,0,-363,-254] 1
86688z (1 curve)	0	2+ 3- 7- 43-	2+ 3-  3 7- -2  1  5  7
Curve Equation t 86688z1 [0,0,0,-19731,-1010522] 1
86688ba (2 curves)	2	2- 3+ 7+ 43+	2- 3+ -4 7+  0 -2  6 -4
Curve Equation t Generators 86688ba1 [0,0,0,-297,2060] 2 [1:42:1]&[7:18:1] 86688ba2 [0,0,0,-4812,128480] 2 [-8:408:1]&[13:261:1]
86688bb (1 curve)	1	2- 3+ 7+ 43-	2- 3+  1 7+ -6  5 -7  7
Curve Equation t Generators 86688bb1 [0,0,0,-39507,-3016998] 1 [-942:387:8]
86688bc (1 curve)	1	2- 3+ 7+ 43-	2- 3+ -1 7+  2 -5 -5  1
Curve Equation t Generators 86688bc1 [0,0,0,-243,-1286] 1 [-10:12:1]
86688bd (2 curves)	1	2- 3+ 7+ 43-	2- 3+  2 7+ -4 -2 -2 -8
Curve Equation t Generators 86688bd1 [0,0,0,-1329,18580] 2 [17:30:1] 86688bd2 [0,0,0,-684,36640] 2 [60:460:1]
86688be (1 curve)	1	2- 3+ 7- 43+	2- 3+  1 7-  2 -5  5 -1
Curve Equation t Generators 86688be1 [0,0,0,-2187,-34722] 1 [69:378:1]
86688bf (1 curve)	1	2- 3+ 7- 43+	2- 3+ -1 7- -6  5  7 -7
Curve Equation t Generators 86688bf1 [0,0,0,-355563,-81458946] 1 [-42295:41714:125]
86688bg (2 curves)	1	2- 3+ 7- 43+	2- 3+ -2 7- -4 -2  2  8
Curve Equation t Generators 86688bg1 [0,0,0,-11961,501660] 2 [33:378:1] 86688bg2 [0,0,0,-6156,989280] 2 [69:945:1]
86688bh (2 curves)	0	2- 3+ 7- 43-	2- 3+  4 7-  0 -2 -6  4
Curve Equation t 86688bh1 [0,0,0,-2673,55620] 2 86688bh2 [0,0,0,-43308,3468960] 2
86688bi (1 curve)	1	2- 3- 7+ 43+	2- 3- -1 7+  0  1  3 -1
Curve Equation t Generators 86688bi1 [0,0,0,-363,254] 1 [-11:54:1]
86688bj (1 curve)	1	2- 3- 7+ 43+	2- 3-  3 7+  2  1  5 -7
Curve Equation t Generators 86688bj1 [0,0,0,-19731,1010522] 1 [194:5913:8]
86688bk (1 curve)	2	2- 3- 7+ 43-	2- 3-  1 7+ -6  1  1 -7
Curve Equation t Generators 86688bk1 [0,0,0,-53787,4801358] 1 [133:-18:1]&[253:2718:1]
86688bl (1 curve)	0	2- 3- 7+ 43-	2- 3- -1 7+  2  7  7 -5
Curve Equation t 86688bl1 [0,0,0,-81003,8859454] 1
86688bm (1 curve)	0	2- 3- 7+ 43-	2- 3-  2 7+ -1 -2  4 -5
Curve Equation t 86688bm1 [0,0,0,-579,6442] 1
86688bn (4 curves)	0	2- 3- 7+ 43-	2- 3-  2 7+ -4 -2 -2  4
Curve Equation t 86688bn1 [0,0,0,-1505829,-702400340] 4 86688bn2 [0,0,0,-178419,-1897334822] 2 86688bn3 [0,0,0,-2916444,822192352] 2 86688bn4 [0,0,0,-24010059,-45283279970] 2
86688bo (2 curves)	0	2- 3- 7+ 43-	2- 3-  2 7+ -4  4 -2 -2
Curve Equation t 86688bo1 [0,0,0,771,772] 2 86688bo2 [0,0,0,-3099,6190] 2
86688bp (4 curves)	2	2- 3- 7+ 43-	2- 3- -2 7+  0 -2 -2 -4
Curve Equation t Generators 86688bp1 [0,0,0,-5421,-153340] 4 [-43:16:1]&[128:1118:1] 86688bp2 [0,0,0,-3531,-261826] 2 [125:1118:1]&[146:1528:1] 86688bp3 [0,0,0,-7356,-34144] 2 [-74:324:1]&[-59:441:1] 86688bp4 [0,0,0,-86691,-9824470] 2 [406:4680:1]&[506:8710:1]
86688bq (1 curve)	2	2- 3- 7+ 43-	2- 3- -2 7+ -3  5 -7  4
Curve Equation t Generators 86688bq1 [0,0,0,-936,11664] 1 [16:-28:1]&[0:108:1]
86688br (2 curves)	2	2- 3- 7- 43+	2- 3-  0 7-  0 -6 -6 -4
Curve Equation t Generators 86688br1 [0,0,0,-45,1188] 2 [-3:36:1]&[37:224:1] 86688br2 [0,0,0,-1980,33696] 2 [30:-36:1]&[-26:260:1]
86688bs (4 curves)	1	2- 3- 7- 43-	2- 3-  2 7-  0 -2 -2  4
Curve Equation t Generators 86688bs1 [0,0,0,-6429,187220] 4 [-17:540:1] 86688bs2 [0,0,0,5181,788618] 2 [26:970:1] 86688bs3 [0,0,0,-19659,-831490] 2 [-67:430:1] 86688bs4 [0,0,0,-101244,12399392] 2 [76:2268:1]
86688bt (1 curve)	1	2- 3- 7- 43-	2- 3- -2 7- -3 -3 -3  4
Curve Equation t Generators 86688bt1 [0,0,0,4344,-1679344] 1 [160:1764:1]

Data from Elliptic Curve Data by J. E. Cremona.
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