Cremona's table of elliptic curves

10115 = 5 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	5+ 7+ 17-	Signs for the Atkin-Lehner involutions
Class	10115d	Isogeny class
Conductor	10115	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	3888	Modular degree for the optimal curve
Δ	20462645 = 5 · 72 · 174	Discriminant
Eigenvalues	-2 -2 5+ 7+ -3  0 17- -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-96,-324]	[a1,a2,a3,a4,a6]
Generators	[-6:8:1] [-4:3:1]	Generators of the group modulo torsion
j	1183744/245	j-invariant
L	2.1914381680156	L(r)(E,1)/r!
Ω	1.5461027332187	Real period
R	0.23623248754542	Regulator
r	2	Rank of the group of rational points
S	1.0000000000007	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	91035bn1 50575x1 70805br1 10115m1	Quadratic twists by: -3 5 -7 17

Hecke Eigenvalues for elliptic curve 10115d1

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	-2	+	+	-3	0	-	-5	-6	9	-4	4	3	-8	-6	-10	-11	-5	-4	-3	2	-9	-12	-5	8

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Quadratic twists for elliptic curve 10115d1

-3	5	-7	17
91035bn1	50575x1	70805br1	10115m1

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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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