Cremona's table of elliptic curves

12540 = 2² · 3 · 5 · 11 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 11+ 19+	Signs for the Atkin-Lehner involutions
Class	12540i	Isogeny class
Conductor	12540	Conductor
∏ cp	114	Product of Tamagawa factors cp
deg	158688	Modular degree for the optimal curve
Δ	-188111553529363200 = -1 · 28 · 319 · 52 · 113 · 19	Discriminant
Eigenvalues	2- 3- 5+ -2 11+  5  7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,110419,-15325425]	[a1,a2,a3,a4,a6]
Generators	[157:2430:1]	Generators of the group modulo torsion
j	581582383072403456/734810755974075	j-invariant
L	5.1362991112673	L(r)(E,1)/r!
Ω	0.17074043648708	Real period
R	0.26388157538419	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	50160bj1 37620n1 62700a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12540i1

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
-	-	+	-2	+	5	7	+	-6	-8	-6	-4	-4	8	0	9	-1	-12	12	-3	-2	-15	3	13	8

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Quadratic twists for elliptic curve 12540i1

-4	-3	5
50160bj1	37620n1	62700a1

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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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