Cremona's table of elliptic curves

37 = Prime conductor

Field	Data	Notes
Atkin-Lehner	37+	Signs for the Atkin-Lehner involutions
Class	37a	Isogeny class
Conductor	37	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	2	Modular degree for the optimal curve
Δ	37 = Prime discriminant	Discriminant
Eigenvalues	-2 -3 -2 -1 -5 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1,0]	[a1,a2,a3,a4,a6]
Generators	[0:0:1]	Generators of the group modulo torsion
j	110592/37	j-invariant
L	0.30599977383405	L(r)(E,1)/r!
Ω	5.9869172924639	Real period
R	0.051111408239969	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	592c1 2368g1 333d1 925e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 37a1

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	-3	-2	-1	-5	-2	0	0	2	6	-4	+	-9	2	-9	1	8	-8	8	9	-1	4	-15	4	4

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Quadratic twists for elliptic curve 37a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59
592c1	2368g1	333d1	925e1	1813b1	4477a1	6253c1	10693g1	13357d1	19573c1	31117d1	35557d1	1369d1	62197b1	68413c1	81733b1	103933a1	128797b1

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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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