Cremona's table of elliptic curves

21312 = 2⁶ · 3² · 37

Class	r	Atkin-Lehner	Eigenvalues
21312a (2 curves)	1	2+ 3+ 37+	2+ 3+  2  0 -4  6  6  4
Curve Equation t Generators 21312a1 [0,0,0,-144,-728] 2 [161:2037:1] 21312a2 [0,0,0,-2364,-44240] 2 [56259:684335:343]
21312b (1 curve)	1	2+ 3+ 37+	2+ 3+  2 -3  5  3 -3 -5
Curve Equation t Generators 21312b1 [0,0,0,-1644,26032] 1 [6:128:1]
21312c (2 curves)	1	2+ 3+ 37+	2+ 3+ -2  0  4  6 -6  4
Curve Equation t Generators 21312c1 [0,0,0,-1296,19656] 2 [-15:189:1] 21312c2 [0,0,0,-21276,1194480] 2 [133:847:1]
21312d (1 curve)	1	2+ 3+ 37+	2+ 3+ -2 -3 -5  3  3 -5
Curve Equation t Generators 21312d1 [0,0,0,-14796,-702864] 1 [165:1161:1]
21312e (1 curve)	0	2+ 3+ 37-	2+ 3+  2  1  5 -3 -1 -7
Curve Equation t 21312e1 [0,0,0,756,12528] 1
21312f (2 curves)	0	2+ 3+ 37-	2+ 3+  2 -4 -4  2 -6  6
Curve Equation t 21312f1 [0,0,0,756,19440] 2 21312f2 [0,0,0,-7884,237168] 2
21312g (1 curve)	2	2+ 3+ 37-	2+ 3+ -2  1 -5 -3  1 -7
Curve Equation t Generators 21312g1 [0,0,0,84,-464] 1 [5:9:1]&[6:16:1]
21312h (2 curves)	0	2+ 3+ 37-	2+ 3+ -2 -4  4  2  6  6
Curve Equation t 21312h1 [0,0,0,84,-720] 2 21312h2 [0,0,0,-876,-8784] 2
21312i (2 curves)	0	2+ 3- 37+	2+ 3-  0  0  0  6  4 -4
Curve Equation t 21312i1 [0,0,0,-120,8008] 2 21312i2 [0,0,0,-6780,213136] 2
21312j (2 curves)	0	2+ 3- 37+	2+ 3-  0 -1  3  1  3  7
Curve Equation t 21312j1 [0,0,0,1140,57584] 1 21312j2 [0,0,0,-85260,9589232] 1
21312k (3 curves)	0	2+ 3- 37+	2+ 3-  0 -1  3  4 -6 -2
Curve Equation t 21312k1 [0,0,0,-120,-502] 1 21312k2 [0,0,0,-840,9074] 1 21312k3 [0,0,0,-67440,6741002] 1
21312l (1 curve)	0	2+ 3- 37+	2+ 3-  0 -3 -3  0 -2  2
Curve Equation t 21312l1 [0,0,0,-1200,-15968] 1
21312m (4 curves)	0	2+ 3- 37+	2+ 3-  2  0 -4 -6 -6 -8
Curve Equation t 21312m1 [0,0,0,8916,90160] 2 21312m2 [0,0,0,-37164,735280] 4 21312m3 [0,0,0,-348204,-78517712] 2 21312m4 [0,0,0,-463404,121275952] 2
21312n (4 curves)	0	2+ 3- 37+	2+ 3- -2  0 -4  2  6  0
Curve Equation t 21312n1 [0,0,0,-1416,1064] 2 21312n2 [0,0,0,-15996,776720] 4 21312n3 [0,0,0,-9516,1411760] 2 21312n4 [0,0,0,-255756,49783664] 2
21312o (2 curves)	0	2+ 3- 37+	2+ 3-  4  0  0 -2  0  0
Curve Equation t 21312o1 [0,0,0,-408,3080] 2 21312o2 [0,0,0,132,10640] 2
21312p (1 curve)	2	2+ 3- 37+	2+ 3- -4 -1 -3  5 -7 -5
Curve Equation t Generators 21312p1 [0,0,0,-7212,239920] 1 [-90:400:1]&[-28:648:1]
21312q (1 curve)	0	2+ 3- 37+	2+ 3- -4  3  5 -3 -3  7
Curve Equation t 21312q1 [0,0,0,-105014892,-414216952400] 1
21312r (1 curve)	0	2+ 3- 37+	2+ 3- -4 -3  5  0  6 -2
Curve Equation t 21312r1 [0,0,0,-192,160] 1
21312s (2 curves)	1	2+ 3- 37-	2+ 3-  0  0  4  2  0 -6
Curve Equation t Generators 21312s1 [0,0,0,-480,3976] 2 [17:27:1] 21312s2 [0,0,0,-1020,-6608] 2 [-22:72:1]
21312t (1 curve)	1	2+ 3- 37-	2+ 3-  0  3  1 -1  3 -3
Curve Equation t Generators 21312t1 [0,0,0,9780,-2379152] 1 [1661:67797:1]
21312u (2 curves)	1	2+ 3- 37-	2+ 3-  2  4  0 -2 -2 -2
Curve Equation t Generators 21312u1 [0,0,0,-99,-540] 2 [386862:4581585:2744] 21312u2 [0,0,0,-1764,-28512] 2 [564:13356:1]
21312v (2 curves)	1	2+ 3- 37-	2+ 3-  2 -4  0 -2 -2  2
Curve Equation t Generators 21312v1 [0,0,0,-99,540] 2 [66:135:8] 21312v2 [0,0,0,-1764,28512] 2 [21:27:1]
21312w (1 curve)	1	2+ 3- 37-	2+ 3- -2  1  1  6  4  8
Curve Equation t Generators 21312w1 [0,0,0,-336,-2144] 1 [-213:107:27]
21312x (1 curve)	1	2+ 3- 37-	2+ 3- -2 -1 -5  2  0  0
Curve Equation t Generators 21312x1 [0,0,0,-36,-54] 1 [-5:1:1]
21312y (2 curves)	1	2+ 3- 37-	2+ 3- -2 -4 -4  6 -6  2
Curve Equation t Generators 21312y1 [0,0,0,-336,-664] 2 [-14:36:1] 21312y2 [0,0,0,1284,-5200] 2 [13:117:1]
21312z (1 curve)	1	2+ 3- 37-	2+ 3-  4 -1 -1  3 -3  5
Curve Equation t Generators 21312z1 [0,0,0,852,634160] 1 [470:10240:1]
21312ba (1 curve)	1	2+ 3- 37-	2+ 3- -4  1 -3 -2 -8 -2
Curve Equation t Generators 21312ba1 [0,0,0,-522,4590] 1 [13:1:1]
21312bb (1 curve)	1	2+ 3- 37-	2+ 3- -4 -1  3 -2 -8  2
Curve Equation t Generators 21312bb1 [0,0,0,-522,-4590] 1 [-357:17:27]
21312bc (2 curves)	0	2- 3+ 37+	2- 3+  2  0  4  6  6 -4
Curve Equation t 21312bc1 [0,0,0,-144,728] 2 21312bc2 [0,0,0,-2364,44240] 2
21312bd (1 curve)	0	2- 3+ 37+	2- 3+  2  3 -5  3 -3  5
Curve Equation t 21312bd1 [0,0,0,-1644,-26032] 1
21312be (2 curves)	0	2- 3+ 37+	2- 3+ -2  0 -4  6 -6 -4
Curve Equation t 21312be1 [0,0,0,-1296,-19656] 2 21312be2 [0,0,0,-21276,-1194480] 2
21312bf (1 curve)	0	2- 3+ 37+	2- 3+ -2  3  5  3  3  5
Curve Equation t 21312bf1 [0,0,0,-14796,702864] 1
21312bg (1 curve)	1	2- 3+ 37-	2- 3+  2 -1 -5 -3 -1  7
Curve Equation t Generators 21312bg1 [0,0,0,756,-12528] 1 [96:972:1]
21312bh (1 curve)	1	2- 3+ 37-	2- 3+  2  3 -3 -3  5  3
Curve Equation t Generators 21312bh1 [0,0,0,5076,237168] 1 [-26:296:1]
21312bi (1 curve)	1	2- 3+ 37-	2- 3+  2 -3  3 -3  5 -3
Curve Equation t Generators 21312bi1 [0,0,0,5076,-237168] 1 [396:7992:1]
21312bj (2 curves)	1	2- 3+ 37-	2- 3+  2  4  4  2 -6 -6
Curve Equation t Generators 21312bj1 [0,0,0,756,-19440] 2 [40970:744128:125] 21312bj2 [0,0,0,-7884,-237168] 2 [1314:47520:1]
21312bk (1 curve)	1	2- 3+ 37-	2- 3+ -2 -1  5 -3  1  7
Curve Equation t Generators 21312bk1 [0,0,0,84,464] 1 [10:48:1]
21312bl (1 curve)	1	2- 3+ 37-	2- 3+ -2  3  3 -3 -5  3
Curve Equation t Generators 21312bl1 [0,0,0,564,-8784] 1 [21:111:1]
21312bm (1 curve)	1	2- 3+ 37-	2- 3+ -2 -3 -3 -3 -5 -3
Curve Equation t Generators 21312bm1 [0,0,0,564,8784] 1 [90:888:1]
21312bn (2 curves)	1	2- 3+ 37-	2- 3+ -2  4 -4  2  6 -6
Curve Equation t Generators 21312bn1 [0,0,0,84,720] 2 [-3:21:1] 21312bn2 [0,0,0,-876,8784] 2 [10:32:1]
21312bo (2 curves)	1	2- 3- 37+	2- 3-  0  0  0  6  4  4
Curve Equation t Generators 21312bo1 [0,0,0,-120,-8008] 2 [97:945:1] 21312bo2 [0,0,0,-6780,-213136] 2 [14345:90153:125]
21312bp (2 curves)	1	2- 3- 37+	2- 3-  0  1 -3  1  3 -7
Curve Equation t Generators 21312bp1 [0,0,0,1140,-57584] 1 [32:108:1] 21312bp2 [0,0,0,-85260,-9589232] 1 [608:12780:1]
21312bq (3 curves)	1	2- 3- 37+	2- 3-  0  1 -3  4 -6  2
Curve Equation t Generators 21312bq1 [0,0,0,-120,502] 1 [3:13:1] 21312bq2 [0,0,0,-840,-9074] 1 [-2145:2119:125] 21312bq3 [0,0,0,-67440,-6741002] 1 [-88707182804655:7957186159:591646229875]
21312br (1 curve)	1	2- 3- 37+	2- 3-  0  3  3  0 -2 -2
Curve Equation t Generators 21312br1 [0,0,0,-1200,15968] 1 [-7:155:1]
21312bs (4 curves)	1	2- 3- 37+	2- 3-  2  0  4 -6 -6  8
Curve Equation t Generators 21312bs1 [0,0,0,8916,-90160] 2 [373:7425:1] 21312bs2 [0,0,0,-37164,-735280] 4 [530255:9191475:1331] 21312bs3 [0,0,0,-348204,78517712] 2 [-214:11968:1] 21312bs4 [0,0,0,-463404,-121275952] 2 [-29383962800:11013722588:76765625]
21312bt (4 curves)	1	2- 3- 37+	2- 3- -2  0  4  2  6  0
Curve Equation t Generators 21312bt1 [0,0,0,-1416,-1064] 2 [41:99:1] 21312bt2 [0,0,0,-15996,-776720] 4 [1013:31977:1] 21312bt3 [0,0,0,-9516,-1411760] 2 [1285156752:13574100460:6539203] 21312bt4 [0,0,0,-255756,-49783664] 2 [-2665522464:5317124:9129329]
21312bu (2 curves)	1	2- 3- 37+	2- 3-  4  0  0 -2  0  0
Curve Equation t Generators 21312bu1 [0,0,0,-408,-3080] 2 [65:495:1] 21312bu2 [0,0,0,132,-10640] 2 [7945:63063:125]
21312bv (1 curve)	1	2- 3- 37+	2- 3- -4  1  3  5 -7  5
Curve Equation t Generators 21312bv1 [0,0,0,-7212,-239920] 1 [106:432:1]
21312bw (1 curve)	1	2- 3- 37+	2- 3- -4  3 -5  0  6  2
Curve Equation t Generators 21312bw1 [0,0,0,-192,-160] 1 [-7:29:1]
21312bx (1 curve)	1	2- 3- 37+	2- 3- -4 -3 -5 -3 -3 -7
Curve Equation t Generators 21312bx1 [0,0,0,-105014892,414216952400] 1 [634:589824:1]
21312by (2 curves)	0	2- 3- 37-	2- 3-  0  0 -4  2  0  6
Curve Equation t 21312by1 [0,0,0,-480,-3976] 2 21312by2 [0,0,0,-1020,6608] 2
21312bz (1 curve)	0	2- 3- 37-	2- 3-  0  1  1  2  4 -6
Curve Equation t 21312bz1 [0,0,0,-30,-2] 1
21312ca (1 curve)	0	2- 3- 37-	2- 3-  0 -1 -1  2  4  6
Curve Equation t 21312ca1 [0,0,0,-30,2] 1
21312cb (1 curve)	0	2- 3- 37-	2- 3-  0  3  3 -5 -3  1
Curve Equation t 21312cb1 [0,0,0,-300,-3184] 1
21312cc (1 curve)	0	2- 3- 37-	2- 3-  0 -3 -1 -1  3  3
Curve Equation t 21312cc1 [0,0,0,9780,2379152] 1
21312cd (1 curve)	2	2- 3- 37-	2- 3-  0 -3 -3 -5 -3 -1
Curve Equation t Generators 21312cd1 [0,0,0,-300,3184] 1 [-19:45:1]&[-10:72:1]
21312ce (2 curves)	0	2- 3- 37-	2- 3-  0  4  4  2  4  6
Curve Equation t 21312ce1 [0,0,0,-172186995,-869658275144] 2 21312ce2 [0,0,0,-172188660,-869640615488] 2
21312cf (2 curves)	0	2- 3- 37-	2- 3-  0  4 -4  2 -4 -6
Curve Equation t 21312cf1 [0,0,0,-435,-2864] 2 21312cf2 [0,0,0,-2100,34432] 2
21312cg (2 curves)	0	2- 3- 37-	2- 3-  0 -4  4  2 -4  6
Curve Equation t 21312cg1 [0,0,0,-435,2864] 2 21312cg2 [0,0,0,-2100,-34432] 2
21312ch (2 curves)	0	2- 3- 37-	2- 3-  0 -4 -4  2  4 -6
Curve Equation t 21312ch1 [0,0,0,-172186995,869658275144] 2 21312ch2 [0,0,0,-172188660,869640615488] 2
21312ci (1 curve)	0	2- 3- 37-	2- 3- -2  1  5  2  0  0
Curve Equation t 21312ci1 [0,0,0,-36,54] 1
21312cj (1 curve)	0	2- 3- 37-	2- 3- -2 -1 -1  6  4 -8
Curve Equation t 21312cj1 [0,0,0,-336,2144] 1
21312ck (2 curves)	0	2- 3- 37-	2- 3- -2  4  4  6 -6 -2
Curve Equation t 21312ck1 [0,0,0,-336,664] 2 21312ck2 [0,0,0,1284,5200] 2
21312cl (1 curve)	0	2- 3- 37-	2- 3-  4  1  1  3 -3 -5
Curve Equation t 21312cl1 [0,0,0,852,-634160] 1
21312cm (1 curve)	0	2- 3- 37-	2- 3-  4  3  3 -6  4 -6
Curve Equation t 21312cm1 [0,0,0,-2358,44010] 1
21312cn (1 curve)	0	2- 3- 37-	2- 3-  4 -3 -3 -6  4  6
Curve Equation t 21312cn1 [0,0,0,-2358,-44010] 1

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