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
deg	26880	Modular degree for the optimal curve
Δ	9240390477545472 = 228 · 35 · 74 · 59	Discriminant
Eigenvalues	2- 3+ -2 7- -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-267904,-53283295]	[a1,a2,a3,a4,a6]
Generators	[-285:289:1]	Generators of the group modulo torsion
j	2126480513962938771457/9240390477545472	j-invariant
L	3.6384686192894	L(r)(E,1)/r!
Ω	0.20990282821029	Real period
R	2.4762945585769	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	19824v1 79296bc1 7434e1 61950s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2478g1

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 2478g1

-4	8	-3	5	-7
19824v1	79296bc1	7434e1	61950s1	17346be1

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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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