Cremona's table of elliptic curves

2337 = 3 · 19 · 41

Field	Data	Notes
Atkin-Lehner	3+ 19+ 41+	Signs for the Atkin-Lehner involutions
Class	2337a	Isogeny class
Conductor	2337	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4560	Modular degree for the optimal curve
Δ	-2182590434763 = -1 · 35 · 194 · 413	Discriminant
Eigenvalues	-2 3+  0 -2 -5  2  5 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,2872,38336]	[a1,a2,a3,a4,a6]
Generators	[-2:180:1]	Generators of the group modulo torsion
j	2618941474304000/2182590434763	j-invariant
L	1.2452784089261	L(r)(E,1)/r!
Ω	0.53257115810817	Real period
R	1.1691192716384	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	37392q1 7011c1 58425i1 114513q1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 2337a1

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	-5	2	5	+	2	7	3	-3	+	-1	-3	-2	4	5	2	15	13	-14	0	-6	-16

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Quadratic twists for elliptic curve 2337a1

-4	-3	5	-7	-19	41
37392q1	7011c1	58425i1	114513q1	44403f1	95817i1

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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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