Cremona's table of elliptic curves

2331 = 3² · 7 · 37

Field	Data	Notes
Atkin-Lehner	3- 7- 37+	Signs for the Atkin-Lehner involutions
Class	2331g	Isogeny class
Conductor	2331	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	-342314343 = -1 · 36 · 73 · 372	Discriminant
Eigenvalues	-1 3- -4 7- -4  4  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-47,910]	[a1,a2,a3,a4,a6]
Generators	[-2:32:1]	Generators of the group modulo torsion
j	-15438249/469567	j-invariant
L	1.5328745512607	L(r)(E,1)/r!
Ω	1.425974973772	Real period
R	0.35832198541464	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	37296bu1 259a1 58275j1 16317e1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2331g1

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
-1	-	-4	-	-4	4	0	-6	4	6	2	+	6	-4	12	-10	10	-8	-4	0	2	4	0	-16	4

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Quadratic twists for elliptic curve 2331g1

-4	-3	5	-7	37
37296bu1	259a1	58275j1	16317e1	86247p1

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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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