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	2331f	Isogeny class
Conductor	2331	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-15293691 = -1 · 310 · 7 · 37	Discriminant
Eigenvalues	0 3- -3 7-  1 -1  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1524,22900]	[a1,a2,a3,a4,a6]
Generators	[22:4:1]	Generators of the group modulo torsion
j	-536971313152/20979	j-invariant
L	2.2810442831841	L(r)(E,1)/r!
Ω	2.0744337916959	Real period
R	0.54979924939405	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	37296bs1 777c1 58275e1 16317d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2331f1

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
0	-	-3	-	1	-1	2	4	-4	0	3	+	2	10	-10	-9	-5	-2	3	-15	2	-4	2	-7	-3

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Quadratic twists for elliptic curve 2331f1

-4	-3	5	-7	37
37296bs1	777c1	58275e1	16317d1	86247o1

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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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