Cremona's table of elliptic curves

55696 = 2⁴ · 59²

Field	Data	Notes
Atkin-Lehner	2+ 59+	Signs for the Atkin-Lehner involutions
Class	55696a	Isogeny class
Conductor	55696	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	396480	Modular degree for the optimal curve
Δ	-138607933098479024 = -1 · 24 · 599	Discriminant
Eigenvalues	2+ -1  3  1  2  2  2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-136919,-26433038]	[a1,a2,a3,a4,a6]
Generators	[6836633850929153735658:151277998074493090411781:9385625830135078152]	Generators of the group modulo torsion
j	-2048	j-invariant
L	7.2451148911526	L(r)(E,1)/r!
Ω	0.12127422795505	Real period
R	29.87079370993	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	27848a1 55696b1	Quadratic twists by: -4 -59

Hecke Eigenvalues for elliptic curve 55696a1

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	3	1	2	2	2	-1	6	5	4	-10	-5	-12	-2	3	+	10	2	-8	-8	-1	-6	-6	8

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Quadratic twists for elliptic curve 55696a1

-4	-59
27848a1	55696b1

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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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