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	2414f	Isogeny class
Conductor	2414	Conductor
∏ cp	72	Product of Tamagawa factors cp
deg	13392	Modular degree for the optimal curve
Δ	101443309568 = 212 · 173 · 712	Discriminant
Eigenvalues	2-  0  2  0  0 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-515989,142791021]	[a1,a2,a3,a4,a6]
j	15193025018461003992993/101443309568	j-invariant
L	3.2828552245731	L(r)(E,1)/r!
Ω	0.72952338323847	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	19312j1 77248j1 21726j1 60350a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2414f1

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

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Quadratic twists for elliptic curve 2414f1

-4	8	-3	5	-7	17
19312j1	77248j1	21726j1	60350a1	118286n1	41038f1

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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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