Cremona's table of elliptic curves

2312 = 2³ · 17²

Field	Data	Notes
Atkin-Lehner	2+ 17+	Signs for the Atkin-Lehner involutions
Class	2312b	Isogeny class
Conductor	2312	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4352	Modular degree for the optimal curve
Δ	30358496383232 = 28 · 179	Discriminant
Eigenvalues	2+ -2  0  2  2 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-8188,-107904]	[a1,a2,a3,a4,a6]
Generators	[-25:286:1]	Generators of the group modulo torsion
j	2000	j-invariant
L	2.3896787503298	L(r)(E,1)/r!
Ω	0.52865040425595	Real period
R	4.5203384525793	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	4624b1 18496e1 20808bd1 57800v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2312b1

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	2	2	-2	+	-4	-6	8	6	-8	0	12	-8	-6	-4	8	4	6	-8	2	4	-14	-8

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Quadratic twists for elliptic curve 2312b1

-4	8	-3	5	-7	17
4624b1	18496e1	20808bd1	57800v1	113288k1	2312a1

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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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