Cremona's table of elliptic curves

3600 = 2⁴ · 3² · 5²

Class	r	Atkin-Lehner	Eigenvalues
3600a (1 curve)	1	2+ 3+ 5+	2+ 3+ 5+ -1  4 -1 -4 -1
Curve Equation t Generators 3600a1 [0,0,0,-60,-180] 1 [9:3:1]
3600b (1 curve)	1	2+ 3+ 5+	2+ 3+ 5+ -1 -4 -1  4 -1
Curve Equation t Generators 3600b1 [0,0,0,-540,4860] 1 [9:27:1]
3600c (2 curves)	1	2+ 3+ 5+	2+ 3+ 5+  2  2 -4 -2 -4
Curve Equation t Generators 3600c1 [0,0,0,-675,-60750] 2 [99:918:1] 3600c2 [0,0,0,-27675,-1761750] 2 [-95:100:1]
3600d (2 curves)	1	2+ 3+ 5+	2+ 3+ 5+  2 -2 -4  2 -4
Curve Equation t Generators 3600d1 [0,0,0,-75,2250] 2 [-5:50:1] 3600d2 [0,0,0,-3075,65250] 2 [15:150:1]
3600e (1 curve)	0	2+ 3+ 5-	2+ 3+ 5-  1  4  1  4 -1
Curve Equation t 3600e1 [0,0,0,-1500,-22500] 1
3600f (1 curve)	0	2+ 3+ 5-	2+ 3+ 5-  1 -4  1 -4 -1
Curve Equation t 3600f1 [0,0,0,-13500,607500] 1
3600g (2 curves)	0	2+ 3+ 5-	2+ 3+ 5-  4  4  4  6  4
Curve Equation t 3600g1 [0,0,0,-135,1350] 2 3600g2 [0,0,0,-2835,58050] 2
3600h (2 curves)	0	2+ 3+ 5-	2+ 3+ 5-  4 -4  4 -6  4
Curve Equation t 3600h1 [0,0,0,-15,-50] 2 3600h2 [0,0,0,-315,-2150] 2
3600i (2 curves)	0	2+ 3+ 5-	2+ 3+ 5- -4  4 -4 -6  4
Curve Equation t 3600i1 [0,0,0,-3375,168750] 2 3600i2 [0,0,0,-70875,7256250] 2
3600j (2 curves)	0	2+ 3+ 5-	2+ 3+ 5- -4 -4 -4  6  4
Curve Equation t 3600j1 [0,0,0,-375,-6250] 2 3600j2 [0,0,0,-7875,-268750] 2
3600k (6 curves)	0	2+ 3- 5+	2+ 3- 5+  0  4  2  2  4
Curve Equation t 3600k1 [0,0,0,150,875] 2 3600k2 [0,0,0,-975,8750] 4 3600k3 [0,0,0,-5475,-148750] 4 3600k4 [0,0,0,-14475,670250] 2 3600k5 [0,0,0,-86475,-9787750] 2 3600k6 [0,0,0,3525,-589750] 2
3600l (6 curves)	0	2+ 3- 5+	2+ 3- 5+  0 -4 -6 -6  4
Curve Equation t 3600l1 [0,0,0,-3450,77875] 2 3600l2 [0,0,0,-4575,22750] 4 3600l3 [0,0,0,-45075,-3662750] 4 3600l4 [0,0,0,17925,180250] 2 3600l5 [0,0,0,-720075,-235187750] 2 3600l6 [0,0,0,-18075,-8009750] 2
3600m (1 curve)	0	2+ 3- 5+	2+ 3- 5+  2  1 -4  5 -1
Curve Equation t 3600m1 [0,0,0,45,-270] 1
3600n (1 curve)	0	2+ 3- 5+	2+ 3- 5+  3  2  3  6  7
Curve Equation t 3600n1 [0,0,0,60,-20] 1
3600o (4 curves)	0	2+ 3- 5+	2+ 3- 5+  4  0  6 -2 -4
Curve Equation t 3600o1 [0,0,0,825,-4250] 2 3600o2 [0,0,0,-3675,-35750] 4 3600o3 [0,0,0,-48675,-4130750] 2 3600o4 [0,0,0,-30675,2043250] 2
3600p (4 curves)	0	2+ 3- 5+	2+ 3- 5+ -4  4  2  2 -4
Curve Equation t 3600p1 [0,0,0,-450,3375] 2 3600p2 [0,0,0,-1575,-20250] 4 3600p3 [0,0,0,-24075,-1437750] 2 3600p4 [0,0,0,2925,-114750] 2
3600q (1 curve)	0	2+ 3- 5+	2+ 3- 5+ -5 -6  3 -2 -1
Curve Equation t 3600q1 [0,0,0,-52500,5537500] 1
3600r (2 curves)	1	2+ 3- 5-	2+ 3- 5-  2  2  2 -6 -8
Curve Equation t Generators 3600r1 [0,0,0,7125,-193750] 2 [61:684:1] 3600r2 [0,0,0,-37875,-1768750] 2 [-131:972:1]
3600s (2 curves)	1	2+ 3- 5-	2+ 3- 5-  2 -4 -4  0  4
Curve Equation t Generators 3600s1 [0,0,0,-30,-25] 2 [-1:2:1] 3600s2 [0,0,0,-255,1550] 2 [1:36:1]
3600t (1 curve)	1	2+ 3- 5-	2+ 3- 5- -2  1  4 -5 -1
Curve Equation t Generators 3600t1 [0,0,0,1125,-33750] 1 [25:100:1]
3600u (2 curves)	1	2+ 3- 5-	2+ 3- 5- -2  2 -2  6 -8
Curve Equation t Generators 3600u1 [0,0,0,285,-1550] 2 [11:54:1] 3600u2 [0,0,0,-1515,-14150] 2 [-25:90:1]
3600v (2 curves)	1	2+ 3- 5-	2+ 3- 5- -2 -4  4  0  4
Curve Equation t Generators 3600v1 [0,0,0,-750,-3125] 2 [-21:58:1] 3600v2 [0,0,0,-6375,193750] 2 [-75:500:1]
3600w (1 curve)	1	2+ 3- 5-	2+ 3- 5- -3  2 -3 -6  7
Curve Equation t Generators 3600w1 [0,0,0,1500,-2500] 1 [25:225:1]
3600x (1 curve)	1	2+ 3- 5-	2+ 3- 5-  5 -6 -3  2 -1
Curve Equation t Generators 3600x1 [0,0,0,-2100,44300] 1 [49:243:1]
3600y (2 curves)	0	2- 3+ 5+	2- 3+ 5+ -1  0  7  0  7
Curve Equation t 3600y1 [0,0,0,0,-12500] 1 3600y2 [0,0,0,0,337500] 1
3600z (4 curves)	0	2- 3+ 5+	2- 3+ 5+  2  6  4 -6  4
Curve Equation t 3600z1 [0,0,0,-3075,-74750] 2 3600z2 [0,0,0,-51075,-4442750] 2 3600z3 [0,0,0,20925,317250] 2 3600z4 [0,0,0,-87075,2585250] 2
3600ba (4 curves)	0	2- 3+ 5+	2- 3+ 5+  2 -6  4  6  4
Curve Equation t 3600ba1 [0,0,0,2325,-11750] 2 3600ba2 [0,0,0,-9675,-95750] 2 3600ba3 [0,0,0,-27675,2018250] 2 3600ba4 [0,0,0,-459675,119954250] 2
3600bb (4 curves)	0	2- 3+ 5+	2- 3+ 5+ -4  0 -2  0 -8
Curve Equation t 3600bb1 [0,0,0,0,-125] 2 3600bb2 [0,0,0,-375,-2750] 2 3600bb3 [0,0,0,0,3375] 2 3600bb4 [0,0,0,-3375,74250] 2
3600bc (2 curves)	0	2- 3+ 5+	2- 3+ 5+  5  0 -5  0  1
Curve Equation t 3600bc1 [0,0,0,0,-80] 1 3600bc2 [0,0,0,0,2160] 1
3600bd (2 curves)	1	2- 3+ 5-	2- 3+ 5-  1  0 -7  0  7
Curve Equation t Generators 3600bd1 [0,0,0,0,-100] 1 [10:30:1] 3600bd2 [0,0,0,0,2700] 1 [6:54:1]
3600be (2 curves)	1	2- 3+ 5-	2- 3+ 5- -5  0  5  0  1
Curve Equation t Generators 3600be1 [0,0,0,0,-10000] 1 [25:75:1] 3600be2 [0,0,0,0,270000] 1 [-39:459:1]
3600bf (8 curves)	1	2- 3- 5+	2- 3- 5+  0 -4  2  2 -4
Curve Equation t Generators 3600bf1 [0,0,0,-75,40250] 2 [5:200:1] 3600bf2 [0,0,0,-18075,922250] 4 [-65:1350:1] 3600bf3 [0,0,0,-36075,-1219750] 4 [-89:1134:1] 3600bf4 [0,0,0,-288075,59512250] 4 [70:6300:1] 3600bf5 [0,0,0,-486075,-130369750] 4 [815:3850:1] 3600bf6 [0,0,0,125925,-9157750] 2 [511:13734:1] 3600bf7 [0,0,0,-7776075,-8346199750] 2 [146615:56129150:1] 3600bf8 [0,0,0,-396075,-180139750] 2 [1064965:5187350:1331]
3600bg (2 curves)	1	2- 3- 5+	2- 3- 5+ -1  6 -5 -6 -5
Curve Equation t Generators 3600bg1 [0,0,0,-120,-740] 1 [14:18:1] 3600bg2 [0,0,0,-10920,-439220] 1 [194:2178:1]
3600bh (4 curves)	1	2- 3- 5+	2- 3- 5+  2  0 -2 -6  4
Curve Equation t Generators 3600bh1 [0,0,0,-300,1375] 2 [-15:50:1] 3600bh2 [0,0,0,825,9250] 2 [170:2250:1] 3600bh3 [0,0,0,-9300,-345125] 2 [3970:86625:8] 3600bh4 [0,0,0,-8175,-431750] 2 [243430:2724750:1331]
3600bi (4 curves)	1	2- 3- 5+	2- 3- 5+  2 -3  4 -3 -5
Curve Equation t Generators 3600bi1 [0,0,0,-435,4210] 1 [9:32:1] 3600bi2 [0,0,0,3165,-31070] 1 [369:7168:1] 3600bi3 [0,0,0,-1875,-368750] 1 [81:104:1] 3600bi4 [0,0,0,-451875,-116918750] 1 [1097811:11253424:1331]
3600bj (2 curves)	1	2- 3- 5+	2- 3- 5+ -3  2 -1  2  5
Curve Equation t Generators 3600bj1 [0,0,0,240,6320] 1 [1:81:1] 3600bj2 [0,0,0,-30000,-2050000] 1 [289:3663:1]
3600bk (8 curves)	1	2- 3- 5+	2- 3- 5+ -4  0 -2  6  4
Curve Equation t Generators 3600bk1 [0,0,0,5325,459250] 2 [41:864:1] 3600bk2 [0,0,0,-66675,6003250] 4 [-265:2250:1] 3600bk3 [0,0,0,-48675,-13526750] 2 [455:7650:1] 3600bk4 [0,0,0,-246675,-40616750] 2 [-345:1850:1] 3600bk5 [0,0,0,-1038675,407439250] 2 [465:5000:1] 3600bk6 [0,0,0,-1200675,-505430750] 4 [1991:70686:1] 3600bk7 [0,0,0,-19200675,-32383430750] 2 [9250021:548516934:1331] 3600bk8 [0,0,0,-1632675,-109286750] 2 [-895:25200:1]
3600bl (2 curves)	0	2- 3- 5-	2- 3- 5-  1  6  5  6 -5
Curve Equation t 3600bl1 [0,0,0,-3000,-92500] 1 3600bl2 [0,0,0,-273000,-54902500] 1
3600bm (4 curves)	0	2- 3- 5-	2- 3- 5-  2  2 -6  2  0
Curve Equation t 3600bm1 [0,0,0,-435,-4750] 2 3600bm2 [0,0,0,-7635,-256750] 2 3600bm3 [0,0,0,-4035,474050] 2 3600bm4 [0,0,0,-119235,15795650] 2
3600bn (4 curves)	0	2- 3- 5-	2- 3- 5- -2  2  6 -2  0
Curve Equation t 3600bn1 [0,0,0,-10875,-593750] 2 3600bn2 [0,0,0,-190875,-32093750] 2 3600bn3 [0,0,0,-100875,59256250] 2 3600bn4 [0,0,0,-2980875,1974456250] 2
3600bo (4 curves)	0	2- 3- 5-	2- 3- 5- -2 -3 -4  3 -5
Curve Equation t 3600bo1 [0,0,0,-75,-2950] 1 3600bo2 [0,0,0,-18075,-935350] 1 3600bo3 [0,0,0,-10875,526250] 1 3600bo4 [0,0,0,79125,-3883750] 1
3600bp (2 curves)	0	2- 3- 5-	2- 3- 5-  3  2  1 -2  5
Curve Equation t 3600bp1 [0,0,0,-1200,-16400] 1 3600bp2 [0,0,0,6000,790000] 1
3600bq (2 curves)	0	2- 3- 5-	2- 3- 5-  4 -4  0  4  0
Curve Equation t 3600bq1 [0,0,0,-120,475] 2 3600bq2 [0,0,0,105,2050] 2
3600br (2 curves)	0	2- 3- 5-	2- 3- 5- -4 -4  0 -4  0
Curve Equation t 3600br1 [0,0,0,-3000,59375] 2 3600br2 [0,0,0,2625,256250] 2

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations