Cremona's table of elliptic curves

5115 = 3 · 5 · 11 · 31

Field	Data	Notes
Atkin-Lehner	3+ 5- 11- 31-	Signs for the Atkin-Lehner involutions
Class	5115f	Isogeny class
Conductor	5115	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-41904765375 = -1 · 3 · 53 · 112 · 314	Discriminant
Eigenvalues	-1 3+ 5- -4 11- -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,625,8060]	[a1,a2,a3,a4,a6]
Generators	[-10:35:1] [-2:83:1]	Generators of the group modulo torsion
j	26997300089999/41904765375	j-invariant
L	2.8191134003503	L(r)(E,1)/r!
Ω	0.77858737384654	Real period
R	2.4138702947141	Regulator
r	2	Rank of the group of rational points
S	0.99999999999962	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	81840df1 15345e1 25575o1 56265k1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 5115f1

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	+	-	-4	-	-6	-6	-4	-8	-6	-	2	2	-4	0	-10	0	-2	0	12	-2	-16	-4	-10	-6

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Quadratic twists for elliptic curve 5115f1

-4	-3	5	-11
81840df1	15345e1	25575o1	56265k1

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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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