Cremona's table of elliptic curves

2312 = 2³ · 17²

Field	Data	Notes
Atkin-Lehner	2- 17+	Signs for the Atkin-Lehner involutions
Class	2312d	Isogeny class
Conductor	2312	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	14286351239168 = 211 · 178	Discriminant
Eigenvalues	2- -2  0  0 -2 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-13968,604192]	[a1,a2,a3,a4,a6]
j	6097250/289	j-invariant
L	0.69541310268718	L(r)(E,1)/r!
Ω	0.69541310268718	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4624a2 18496d2 20808h2 57800d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2312d2

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	-2	-6	+	4	-4	0	8	4	-6	8	-8	10	0	-12	8	-12	-2	4	16	10	18

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Quadratic twists for elliptic curve 2312d2

-4	8	-3	5	-7	17
4624a2	18496d2	20808h2	57800d2	113288w2	136b2

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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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