Cremona's table of elliptic curves

8970 = 2 · 3 · 5 · 13 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13+ 23+	Signs for the Atkin-Lehner involutions
Class	8970i	Isogeny class
Conductor	8970	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	24576	Modular degree for the optimal curve
Δ	-57316147200 = -1 · 216 · 32 · 52 · 132 · 23	Discriminant
Eigenvalues	2- 3+ 5+ -4 -6 13+ -8 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-3316,73013]	[a1,a2,a3,a4,a6]
Generators	[1198:-14373:8] [-41:397:1]	Generators of the group modulo torsion
j	-4032510095423809/57316147200	j-invariant
L	6.2342224373752	L(r)(E,1)/r!
Ω	1.1176899644729	Real period
R	0.17430544906059	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	71760bq1 26910t1 44850bc1 116610q1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8970i1

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
-	+	+	-4	-6	+	-8	-8	+	-6	-8	8	6	-6	0	0	4	2	-8	-4	2	2	-14	-14	0

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Quadratic twists for elliptic curve 8970i1

-4	-3	5	13
71760bq1	26910t1	44850bc1	116610q1

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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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