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	10115l	Isogeny class
Conductor	10115	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5184	Modular degree for the optimal curve
Δ	790234375 = 58 · 7 · 172	Discriminant
Eigenvalues	1 -1 5- 7-  6 -6 17+ -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-252,-851]	[a1,a2,a3,a4,a6]
Generators	[-12:31:1]	Generators of the group modulo torsion
j	6161940649/2734375	j-invariant
L	4.6502558933724	L(r)(E,1)/r!
Ω	1.2478983517967	Real period
R	0.46580876225586	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	91035z1 50575c1 70805i1 10115c1	Quadratic twists by: -3 5 -7 17

Hecke Eigenvalues for elliptic curve 10115l1

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 10115l1

-3	5	-7	17
91035z1	50575c1	70805i1	10115c1

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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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