Cremona's table of elliptic curves

2556 = 2² · 3² · 71

Field	Data	Notes
Atkin-Lehner	2- 3+ 71+	Signs for the Atkin-Lehner involutions
Class	2556a	Isogeny class
Conductor	2556	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1584	Modular degree for the optimal curve
Δ	22359888 = 24 · 39 · 71	Discriminant
Eigenvalues	2- 3+  4  2  4  6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-648,6345]	[a1,a2,a3,a4,a6]
j	95551488/71	j-invariant
L	3.1880371509159	L(r)(E,1)/r!
Ω	2.1253581006106	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10224k1 40896e1 2556b1 63900a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2556a1

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
-	+	4	2	4	6	-6	-4	8	0	-2	-6	-6	8	0	-6	-4	-6	-14	+	-14	-8	16	-12	6

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Quadratic twists for elliptic curve 2556a1

-4	8	-3	5	-7
10224k1	40896e1	2556b1	63900a1	125244b1

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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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