Cremona's table of elliptic curves

37 = Prime conductor

Field	Data	Notes
Atkin-Lehner	37-	Signs for the Atkin-Lehner involutions
Class	37b	Isogeny class
Conductor	37	Conductor
∏ cp	1	Product of Tamagawa factors cp
Δ	37 = Prime discriminant	Discriminant
Eigenvalues	0  1  0 -1  3 -4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1873,-31833]	[a1,a2,a3,a4,a6]
j	727057727488000/37	j-invariant
L	0.72568106193615	L(r)(E,1)/r!
Ω	0.72568106193615	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	592e3 2368c3 333a3 925b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 37b2

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	1	0	-1	3	-4	6	2	6	-6	-4	-	-9	8	3	-3	12	8	-4	-15	11	-10	9	6	8

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Quadratic twists for elliptic curve 37b2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53	-59
592e3	2368c3	333a3	925b3	1813c3	4477b3	6253a3	10693a3	13357a3	19573a3	31117a3	35557a3	1369a3	62197c3	68413a3	81733c3	103933b3	128797a3

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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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