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	8970l	Isogeny class
Conductor	8970	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1642456054687500 = 22 · 32 · 516 · 13 · 23	Discriminant
Eigenvalues	2- 3+ 5+ -4  0 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-65546,6130379]	[a1,a2,a3,a4,a6]
Generators	[193:749:1]	Generators of the group modulo torsion
j	31143162165402407329/1642456054687500	j-invariant
L	4.54059383571	L(r)(E,1)/r!
Ω	0.46736259880099	Real period
R	4.8576777938145	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	71760bt3 26910v3 44850u3 116610o3	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8970l4

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	0	-	2	0	+	-2	0	2	2	12	0	-2	4	-10	-8	0	-14	0	16	-10	14

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Quadratic twists for elliptic curve 8970l4

-4	-3	5	13
71760bt3	26910v3	44850u3	116610o3

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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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