Cremona's table of elliptic curves

372 = 2² · 3 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 31+	Signs for the Atkin-Lehner involutions
Class	372d	Isogeny class
Conductor	372	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-40176 = -1 · 24 · 34 · 31	Discriminant
Eigenvalues	2- 3- -3 -5  2 -4 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2,9]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	-87808/2511	j-invariant
L	1.6984822679502	L(r)(E,1)/r!
Ω	3.0344782146121	Real period
R	0.046643995766483	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	1488l1 5952d1 1116b1 9300b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 372d1

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
-	-	-3	-5	2	-4	-4	-5	4	10	+	-6	-5	2	-4	-12	5	-8	12	9	-10	-2	10	-6	-15

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Quadratic twists for elliptic curve 372d1

-4	8	-3	5	-7	-11	13	17	-31
1488l1	5952d1	1116b1	9300b1	18228h1	45012h1	62868l1	107508g1	11532d1

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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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