Cremona's table of elliptic curves

31005 = 3² · 5 · 13 · 53

Class	r	Atkin-Lehner	Eigenvalues
31005a (2 curves)	1	3+ 5+ 13+ 53+	1 3+ 5+ -4 -6 13+  2 -8
Curve Equation t Generators 31005a1 [1,-1,0,-555,-5824] 2 [494:3263:8] 31005a2 [1,-1,0,-9330,-344539] 2 [910:1443:8]
31005b (1 curve)	0	3+ 5+ 13- 53+	0 3+ 5+  4 -2 13-  3  6
Curve Equation t 31005b1 [0,0,1,-537408,151689773] 1
31005c (2 curves)	1	3+ 5+ 13- 53-	0 3+ 5+  2  3 13-  0 -1
Curve Equation t Generators 31005c1 [0,0,1,3702,72528] 3 [18:2271:8] 31005c2 [0,0,1,-37638,-3945031] 1 [895974:57640517:216]
31005d (2 curves)	1	3+ 5+ 13- 53-	0 3+ 5+ -4 -6 13- -3  2
Curve Equation t Generators 31005d1 [0,0,1,64692,-10012101] 3 [137:1192:1] 31005d2 [0,0,1,-2353698,-1394343322] 1 [21714:884111:8]
31005e (2 curves)	1	3+ 5- 13+ 53-	-1 3+ 5- -4  6 13+ -2 -8
Curve Equation t Generators 31005e1 [1,-1,1,-62,236] 2 [4:-9:1] 31005e2 [1,-1,1,-1037,13106] 2 [-21:169:1]
31005f (2 curves)	1	3+ 5- 13- 53+	0 3+ 5-  2 -3 13-  0 -1
Curve Equation t Generators 31005f1 [0,0,1,-4182,146112] 3 [-254:3971:8] 31005f2 [0,0,1,33318,-1958263] 1 [237:-4388:1]
31005g (2 curves)	1	3+ 5- 13- 53+	0 3+ 5- -4  6 13-  3  2
Curve Equation t Generators 31005g1 [0,0,1,-261522,51642345] 3 [-7:7312:1] 31005g2 [0,0,1,582228,270326720] 1 [-222:11407:1]
31005h (1 curve)	0	3+ 5- 13- 53-	0 3+ 5-  4  2 13- -3  6
Curve Equation t 31005h1 [0,0,1,-59712,-5618140] 1
31005i (2 curves)	0	3- 5+ 13+ 53+	1 3- 5+  0  2 13+  6  6
Curve Equation t 31005i1 [1,-1,0,-24345,1474200] 2 31005i2 [1,-1,0,-389970,93831075] 2
31005j (1 curve)	0	3- 5+ 13+ 53+	1 3- 5+ -2 -1 13+  0  0
Curve Equation t 31005j1 [1,-1,0,-360,-3159] 1
31005k (1 curve)	2	3- 5+ 13+ 53+	-2 3- 5+ -2  0 13+ -3  2
Curve Equation t Generators 31005k1 [0,0,1,-363,2704] 1 [-2:58:1]&[-142:473:8]
31005l (2 curves)	1	3- 5+ 13+ 53-	1 3- 5+  4 -2 13+  2  6
Curve Equation t Generators 31005l1 [1,-1,0,1440,42691] 2 [1140:16811:64] 31005l2 [1,-1,0,-13185,501916] 2 [8:626:1]
31005m (1 curve)	1	3- 5+ 13+ 53-	-2 3- 5+ -2  1 13+ -4  3
Curve Equation t Generators 31005m1 [0,0,1,-613443,-212015102] 1 [9191:877812:1]
31005n (2 curves)	0	3- 5- 13+ 53-	1 3- 5- -2 -4 13+  6  6
Curve Equation t 31005n1 [1,-1,0,-8154,284575] 2 31005n2 [1,-1,0,-4509,537538] 2
31005o (2 curves)	2	3- 5- 13+ 53-	-1 3- 5- -2 -2 13+ -6  0
Curve Equation t Generators 31005o1 [1,-1,1,-3227,71354] 2 [-48:361:1]&[24:73:1] 31005o2 [1,-1,1,-3182,73406] 2 [-54:319:1]&[1:264:1]
31005p (1 curve)	0	3- 5- 13+ 53-	2 3- 5- -2 -5 13+ -4  1
Curve Equation t 31005p1 [0,0,1,-31197,14152567] 1
31005q (4 curves)	1	3- 5- 13- 53-	-1 3- 5-  4  4 13-  2 -4
Curve Equation t Generators 31005q1 [1,-1,1,-7952,330986] 4 [-56:801:1] 31005q2 [1,-1,1,-134357,18988364] 4 [-228:6256:1] 31005q3 [1,-1,1,-141512,16859036] 2 [124:1036:1] 31005q4 [1,-1,1,-2149682,1213673024] 2 [1839:58048:1]

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

Part of Computational Number Theory
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