Cremona's table of elliptic curves

13640 = 2³ · 5 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 5+ 11+ 31+	Signs for the Atkin-Lehner involutions
Class	13640c	Isogeny class
Conductor	13640	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	193536	Modular degree for the optimal curve
Δ	6437465145031250000 = 24 · 59 · 118 · 312	Discriminant
Eigenvalues	2+  2 5+  0 11+  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-499751,60077876]	[a1,a2,a3,a4,a6]
Generators	[-96534889:-1569070533:148877]	Generators of the group modulo torsion
j	862711553000150800384/402341571564453125	j-invariant
L	6.1903337730146	L(r)(E,1)/r!
Ω	0.21256279409449	Real period
R	14.561188375852	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27280e1 109120o1 122760bz1 68200q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13640c1

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
+	2	+	0	+	0	0	-4	2	10	+	4	-6	2	4	-4	-4	-14	12	0	4	0	-6	-18	-2

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Quadratic twists for elliptic curve 13640c1

-4	8	-3	5
27280e1	109120o1	122760bz1	68200q1

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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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