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	7	Product of Tamagawa factors cp
Δ	12845952 = 27 · 35 · 7 · 59	Discriminant
Eigenvalues	2- 3+ -2 7- -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-68511744,-218299350495]	[a1,a2,a3,a4,a6]
Generators	[31511:5361297:1]	Generators of the group modulo torsion
j	35564669815710772986504708097/12845952	j-invariant
L	3.6384686192894	L(r)(E,1)/r!
Ω	0.052475707052573	Real period
R	9.9051782343078	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19824v3 79296bc4 7434e3 61950s4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2478g3

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 2478g3

-4	8	-3	5	-7
19824v3	79296bc4	7434e3	61950s4	17346be3

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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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