Cremona's table of elliptic curves

12740 = 2² · 5 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 7- 13-	Signs for the Atkin-Lehner involutions
Class	12740f	Isogeny class
Conductor	12740	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-2548000000 = -1 · 28 · 56 · 72 · 13	Discriminant
Eigenvalues	2-  0 5- 7- -5 13-  7  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-287,-3066]	[a1,a2,a3,a4,a6]
Generators	[23:50:1]	Generators of the group modulo torsion
j	-208417104/203125	j-invariant
L	4.5845209694355	L(r)(E,1)/r!
Ω	0.557869315836	Real period
R	0.45655066909606	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50960ca1 114660bf1 63700k1 12740a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12740f1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	0	-	-	-5	-	7	1	-4	-5	8	4	0	-6	13	-13	-3	-1	5	-3	-16	4	-4	10	-2

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Quadratic twists for elliptic curve 12740f1

-4	-3	5	-7
50960ca1	114660bf1	63700k1	12740a1

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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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