Cremona's table of elliptic curves

2562 = 2 · 3 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 61+	Signs for the Atkin-Lehner involutions
Class	2562a	Isogeny class
Conductor	2562	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-71736 = -1 · 23 · 3 · 72 · 61	Discriminant
Eigenvalues	2+ 3+  1 7+  0 -4  3  6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,12]	[a1,a2,a3,a4,a6]
Generators	[1:3:1]	Generators of the group modulo torsion
j	-1771561/71736	j-invariant
L	2.1210173034755	L(r)(E,1)/r!
Ω	2.8757968081633	Real period
R	0.36877036956414	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	20496x1 81984y1 7686p1 64050cj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2562a1

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	+	0	-4	3	6	-7	2	4	-1	2	-7	-6	4	4	+	-8	5	-11	-4	-17	-1	5

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Quadratic twists for elliptic curve 2562a1

-4	8	-3	5	-7
20496x1	81984y1	7686p1	64050cj1	17934n1

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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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