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	10115c	Isogeny class
Conductor	10115	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	88128	Modular degree for the optimal curve
Δ	19074336752734375 = 58 · 7 · 178	Discriminant
Eigenvalues	1  1 5+ 7+ -6 -6 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-72979,-3670469]	[a1,a2,a3,a4,a6]
Generators	[3203:179023:1] [-626:10309:8]	Generators of the group modulo torsion
j	6161940649/2734375	j-invariant
L	7.3122992381297	L(r)(E,1)/r!
Ω	0.30265980673482	Real period
R	4.0266877615368	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	91035bm1 50575v1 70805bp1 10115l1	Quadratic twists by: -3 5 -7 17

Hecke Eigenvalues for elliptic curve 10115c1

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	1	+	+	-6	-6	-	-5	0	-9	-7	10	0	4	-3	5	-11	10	2	-12	-16	12	-15	-2	2

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Quadratic twists for elliptic curve 10115c1

-3	5	-7	17
91035bm1	50575v1	70805bp1	10115l1

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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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