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	2414b	Isogeny class
Conductor	2414	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	46619168 = 25 · 172 · 712	Discriminant
Eigenvalues	2+  2  0  0  0 -4 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-145,-651]	[a1,a2,a3,a4,a6]
Generators	[33:162:1]	Generators of the group modulo torsion
j	340799721625/46619168	j-invariant
L	3.1588580340632	L(r)(E,1)/r!
Ω	1.387040357762	Real period
R	2.2774088845981	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	19312h2 77248d2 21726y2 60350j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2414b2

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

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Quadratic twists for elliptic curve 2414b2

-4	8	-3	5	-7	17
19312h2	77248d2	21726y2	60350j2	118286e2	41038e2

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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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