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	10115m	Isogeny class
Conductor	10115	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	66096	Modular degree for the optimal curve
Δ	493918505610005 = 5 · 72 · 1710	Discriminant
Eigenvalues	-2  2 5- 7-  3  0 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-27840,-1423724]	[a1,a2,a3,a4,a6]
Generators	[-88:580:1]	Generators of the group modulo torsion
j	1183744/245	j-invariant
L	3.7048731672863	L(r)(E,1)/r!
Ω	0.37498499277157	Real period
R	4.9400285860816	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	91035bb1 50575f1 70805t1 10115d1	Quadratic twists by: -3 5 -7 17

Hecke Eigenvalues for elliptic curve 10115m1

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 10115m1

-3	5	-7	17
91035bb1	50575f1	70805t1	10115d1

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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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