Cremona's table of elliptic curves

10556 = 2² · 7 · 13 · 29

Field	Data	Notes
Atkin-Lehner	2- 7+ 13- 29-	Signs for the Atkin-Lehner involutions
Class	10556c	Isogeny class
Conductor	10556	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	322560	Modular degree for the optimal curve
Δ	-730807405458760448 = -1 · 28 · 77 · 132 · 295	Discriminant
Eigenvalues	2-  3 -4 7+ -4 13- -2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,88568,39859220]	[a1,a2,a3,a4,a6]
j	300133353018138624/2854716427573283	j-invariant
L	2.0916738392124	L(r)(E,1)/r!
Ω	0.20916738392124	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	42224q1 95004f1 73892k1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 10556c1

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
-	3	-4	+	-4	-	-2	-1	3	-	-4	8	-3	-4	-1	13	0	-6	-5	-9	3	10	0	-9	-1

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Quadratic twists for elliptic curve 10556c1

-4	-3	-7
42224q1	95004f1	73892k1

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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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