Cremona's table of elliptic curves

592 = 2⁴ · 37

Field	Data	Notes
Atkin-Lehner	2+ 37+	Signs for the Atkin-Lehner involutions
Class	592a	Isogeny class
Conductor	592	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	9472 = 28 · 37	Discriminant
Eigenvalues	2+  1 -2 -1 -1 -6 -4  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-9,-13]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	351232/37	j-invariant
L	2.1008484302888	L(r)(E,1)/r!
Ω	2.7500416450428	Real period
R	0.76393331500117	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	296a1 2368o1 5328c1 14800g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 592a1

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
+	1	-2	-1	-1	-6	-4	8	-6	2	4	+	7	-2	-9	-3	12	4	0	-7	7	0	-3	-12	-8

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Quadratic twists for elliptic curve 592a1

-4	8	-3	5	-7	-11	13	37
296a1	2368o1	5328c1	14800g1	29008e1	71632a1	100048c1	21904b1

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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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