Cremona's table of elliptic curves

55696 = 2⁴ · 59²

Field	Data	Notes
Atkin-Lehner	2- 59-	Signs for the Atkin-Lehner involutions
Class	55696p	Isogeny class
Conductor	55696	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1002240	Modular degree for the optimal curve
Δ	-1.0438160877382E+19	Discriminant
Eigenvalues	2-  1  1 -3  2  6 -2  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1393560,651530132]	[a1,a2,a3,a4,a6]
Generators	[1462:41728:1]	Generators of the group modulo torsion
j	-1732323601/60416	j-invariant
L	7.5536716952082	L(r)(E,1)/r!
Ω	0.22707885608234	Real period
R	4.1580664012063	Regulator
r	1	Rank of the group of rational points
S	1.0000000000007	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6962c1 944h1	Quadratic twists by: -4 -59

Hecke Eigenvalues for elliptic curve 55696p1

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	1	-3	2	6	-2	5	4	-5	2	-8	7	-6	-2	9	-	8	-2	-12	-4	-5	14	0	-8

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Quadratic twists for elliptic curve 55696p1

-4	-59
6962c1	944h1

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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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