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
Δ	121433985532928 = 210 · 179	Discriminant
Eigenvalues	2+ -2  0  2  2 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-106448,-13392656]	[a1,a2,a3,a4,a6]
Generators	[-249447:130286:1331]	Generators of the group modulo torsion
j	1098500	j-invariant
L	2.3896787503298	L(r)(E,1)/r!
Ω	0.26432520212798	Real period
R	9.0406769051587	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	4624b2 18496e2 20808bd2 57800v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2312b2

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 2312b2

-4	8	-3	5	-7	17
4624b2	18496e2	20808bd2	57800v2	113288k2	2312a2

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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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