Cremona's table of elliptic curves

6970 = 2 · 5 · 17 · 41

Field	Data	Notes
Atkin-Lehner	2- 5+ 17- 41-	Signs for the Atkin-Lehner involutions
Class	6970f	Isogeny class
Conductor	6970	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-22463808160000 = -1 · 28 · 54 · 174 · 412	Discriminant
Eigenvalues	2- -2 5+ -2 -6 -6 17- -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-4806,261220]	[a1,a2,a3,a4,a6]
Generators	[120:-1250:1] [-82:366:1]	Generators of the group modulo torsion
j	-12276672184572769/22463808160000	j-invariant
L	5.1553147961086	L(r)(E,1)/r!
Ω	0.60501717453986	Real period
R	0.26627936223618	Regulator
r	2	Rank of the group of rational points
S	0.99999999999991	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	55760s2 62730n2 34850f2 118490t2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 6970f2

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
-	-2	+	-2	-6	-6	-	-6	0	-6	-4	-6	-	-12	-10	2	4	14	-10	2	14	10	8	-14	-14

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Quadratic twists for elliptic curve 6970f2

-4	-3	5	17
55760s2	62730n2	34850f2	118490t2

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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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