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	10115g	Isogeny class
Conductor	10115	Conductor
∏ cp	3	Product of Tamagawa factors cp
Δ	-1034898270875 = -1 · 53 · 73 · 176	Discriminant
Eigenvalues	0 -1 5- 7+  3  5 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,2505,-9069]	[a1,a2,a3,a4,a6]
j	71991296/42875	j-invariant
L	1.5343291505578	L(r)(E,1)/r!
Ω	0.51144305018594	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	91035d2 50575m2 70805e2 35a1	Quadratic twists by: -3 5 -7 17

Hecke Eigenvalues for elliptic curve 10115g2

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	-1	-	+	3	5	+	2	6	-3	4	-2	12	-10	9	12	0	-8	-4	0	-2	1	12	-12	1

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Quadratic twists for elliptic curve 10115g2

-3	5	-7	17
91035d2	50575m2	70805e2	35a1

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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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