Cremona's table of elliptic curves

2414 = 2 · 17 · 71

Field	Data	Notes
Atkin-Lehner	2- 17- 71-	Signs for the Atkin-Lehner involutions
Class	2414g	Isogeny class
Conductor	2414	Conductor
∏ cp	9	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	-2790584 = -1 · 23 · 173 · 71	Discriminant
Eigenvalues	2-  3 -1  3  0 -5 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-243,-1397]	[a1,a2,a3,a4,a6]
j	-1580759992449/2790584	j-invariant
L	5.4425730529213	L(r)(E,1)/r!
Ω	0.60473033921348	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	19312k1 77248m1 21726g1 60350b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2414g1

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
-	3	-1	3	0	-5	-	4	5	1	-5	-2	-2	4	2	9	-11	10	-4	-	-14	0	-4	-18	-1

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Quadratic twists for elliptic curve 2414g1

-4	8	-3	5	-7	17
19312k1	77248m1	21726g1	60350b1	118286s1	41038k1

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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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