Cremona's table of elliptic curves

3115 = 5 · 7 · 89

Field	Data	Notes
Atkin-Lehner	5+ 7- 89+	Signs for the Atkin-Lehner involutions
Class	3115b	Isogeny class
Conductor	3115	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-142696839753125 = -1 · 55 · 78 · 892	Discriminant
Eigenvalues	1  0 5+ 7-  0 -4  2  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,12215,242550]	[a1,a2,a3,a4,a6]
j	201550614533598231/142696839753125	j-invariant
L	1.4729703379163	L(r)(E,1)/r!
Ω	0.36824258447907	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	49840i2 28035k2 15575a2 21805h2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3115b2

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

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Quadratic twists for elliptic curve 3115b2

-4	-3	5	-7
49840i2	28035k2	15575a2	21805h2

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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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