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	2331a	Isogeny class
Conductor	2331	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-797136798799467 = -1 · 311 · 74 · 374	Discriminant
Eigenvalues	-1 3-  2 7+  0 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-914,1358660]	[a1,a2,a3,a4,a6]
Generators	[-30:1180:1]	Generators of the group modulo torsion
j	-115714886617/1093466116323	j-invariant
L	2.2162519074875	L(r)(E,1)/r!
Ω	0.40277099550395	Real period
R	1.3756277960845	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	37296cm3 777e4 58275o3 16317i4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2331a4

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	-	2	+	0	-2	-2	-4	8	6	-8	-	-6	-4	-8	-6	0	-2	12	12	2	16	-12	-10	-14

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Quadratic twists for elliptic curve 2331a4

-4	-3	5	-7	37
37296cm3	777e4	58275o3	16317i4	86247e3

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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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