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	10115k	Isogeny class
Conductor	10115	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16320	Modular degree for the optimal curve
Δ	-4150575677395 = -1 · 5 · 7 · 179	Discriminant
Eigenvalues	0  0 5- 7- -2 -5 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-19652,-1064893]	[a1,a2,a3,a4,a6]
Generators	[10003735:113834881:42875]	Generators of the group modulo torsion
j	-7077888/35	j-invariant
L	3.4712779701274	L(r)(E,1)/r!
Ω	0.2015530697256	Real period
R	8.6113249846636	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	91035t1 50575a1 70805d1 10115a1	Quadratic twists by: -3 5 -7 17

Hecke Eigenvalues for elliptic curve 10115k1

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
0	0	-	-	-2	-5	+	4	-5	6	3	7	-3	6	1	4	-6	-1	14	-4	-10	10	9	-4	-2

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Quadratic twists for elliptic curve 10115k1

-3	5	-7	17
91035t1	50575a1	70805d1	10115a1

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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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