Cremona's table of elliptic curves

12710 = 2 · 5 · 31 · 41

Class	r	Atkin-Lehner	Eigenvalues
12710a (2 curves)	1	2+ 5+ 31+ 41+	2+  0 5+  2 -4 -2  2 -4
Curve Equation t Generators 12710a1 [1,-1,0,20,0] 2 [1:4:1] 12710a2 [1,-1,0,-80,60] 2 [-7:19:1]
12710b (2 curves)	0	2+ 5- 31+ 41+	2+  0 5- -2  2  2  6  0
Curve Equation t 12710b1 [1,-1,0,-1229,-14315] 2 12710b2 [1,-1,0,1871,-76935] 2
12710c (2 curves)	0	2+ 5- 31+ 41+	2+ -2 5-  4 -6  0 -2 -2
Curve Equation t 12710c1 [1,0,1,-1025068,-399547542] 2 12710c2 [1,0,1,-16401068,-25566984342] 2
12710d (2 curves)	1	2+ 5- 31+ 41-	2+  0 5- -2  2  2  0  6
Curve Equation t Generators 12710d1 [1,-1,0,-1379909,-623567787] 2 [3194:164371:1] 12710d2 [1,-1,0,-1380709,-622807947] 2 [4251269:218775416:1331]
12710e (2 curves)	1	2+ 5- 31+ 41-	2+  0 5- -2  2 -6  0 -2
Curve Equation t Generators 12710e1 [1,-1,0,-3334154,2342179828] 2 [1017:1054:1] 12710e2 [1,-1,0,-53334154,149932179828] 2 [4217:-2071:1]
12710f (2 curves)	1	2+ 5- 31+ 41-	2+  0 5-  4  2  0 -6 -8
Curve Equation t Generators 12710f1 [1,-1,0,-104,-372] 2 [-6:6:1] 12710f2 [1,-1,0,-1654,-25482] 2 [69:396:1]
12710g (2 curves)	1	2+ 5- 31+ 41-	2+ -2 5-  0 -2 -4  0  0
Curve Equation t Generators 12710g1 [1,0,1,-203,1398] 2 [-1:40:1] 12710g2 [1,0,1,-3483,78806] 2 [-5:312:1]
12710h (2 curves)	1	2+ 5- 31- 41+	2+  2 5-  2  0 -4 -4  0
Curve Equation t Generators 12710h1 [1,1,0,-795667,-273442131] 2 [-4761141:4735408:9261] 12710h2 [1,1,0,-898067,-198710611] 2 [-18555:271739:27]
12710i (2 curves)	1	2+ 5- 31- 41+	2+  2 5- -2 -4  0  0  4
Curve Equation t Generators 12710i1 [1,1,0,-847,-9819] 2 [702:18249:1] 12710i2 [1,1,0,-1247,-139] 2 [-35:64:1]
12710j (2 curves)	1	2+ 5- 31- 41+	2+ -2 5-  0  2  4  2 -2
Curve Equation t Generators 12710j1 [1,0,1,-1088,11406] 2 [30:62:1] 12710j2 [1,0,1,-5088,-129394] 2 [-40:122:1]
12710k (2 curves)	2	2+ 5- 31- 41-	2+ -2 5-  0 -6 -4 -4  0
Curve Equation t Generators 12710k1 [1,0,1,-493,4056] 2 [-25:42:1]&[-20:87:1] 12710k2 [1,0,1,127,13728] 2 [-12:108:1]&[-11:110:1]
12710l (2 curves)	0	2- 5+ 31+ 41+	2- -2 5+  0  2 -4  6  0
Curve Equation t 12710l1 [1,0,0,669,12061] 2 12710l2 [1,0,0,-5581,133311] 2
12710m (4 curves)	0	2- 5- 31+ 41-	2-  0 5- -4  0  6 -6  8
Curve Equation t 12710m1 [1,-1,1,-20527,1137079] 4 12710m2 [1,-1,1,-20607,1127831] 4 12710m3 [1,-1,1,-41107,-1471569] 2 12710m4 [1,-1,1,-1387,3134399] 4

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