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
deg	2304	Modular degree for the optimal curve
Δ	420186801152 = 210 · 177	Discriminant
Eigenvalues	2- -2  0  0 -2 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2408,-33920]	[a1,a2,a3,a4,a6]
j	62500/17	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	4624a1 18496d1 20808h1 57800d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2312d1

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 2312d1

-4	8	-3	5	-7	17
4624a1	18496d1	20808h1	57800d1	113288w1	136b1

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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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