Cremona's table of elliptic curves

2478 = 2 · 3 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 59+	Signs for the Atkin-Lehner involutions
Class	2478g	Isogeny class
Conductor	2478	Conductor
∏ cp	112	Product of Tamagawa factors cp
Δ	165018482786304 = 214 · 310 · 72 · 592	Discriminant
Eigenvalues	2- 3+ -2 7- -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4281984,-3412265439]	[a1,a2,a3,a4,a6]
Generators	[2837:83925:1]	Generators of the group modulo torsion
j	8682780835539571156494337/165018482786304	j-invariant
L	3.6384686192894	L(r)(E,1)/r!
Ω	0.10495141410515	Real period
R	4.9525891171539	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	19824v2 79296bc2 7434e2 61950s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2478g2

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	-	-4	-2	6	4	0	-6	-4	2	-2	-8	0	-14	+	-10	0	-8	14	-8	-12	-6	14

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Quadratic twists for elliptic curve 2478g2

-4	8	-3	5	-7
19824v2	79296bc2	7434e2	61950s2	17346be2

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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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