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	6970h	Isogeny class
Conductor	6970	Conductor
∏ cp	250	Product of Tamagawa factors cp
deg	20000	Modular degree for the optimal curve
Δ	-238677961700000 = -1 · 25 · 55 · 175 · 412	Discriminant
Eigenvalues	2- -1 5- -2  2 -1 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2345,743607]	[a1,a2,a3,a4,a6]
Generators	[-93:456:1]	Generators of the group modulo torsion
j	-1426145474814481/238677961700000	j-invariant
L	5.08706325782	L(r)(E,1)/r!
Ω	0.45490100468477	Real period
R	1.1182791872146	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	5	Number of elements in the torsion subgroup
Twists	55760ba1 62730h1 34850d1 118490n1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 6970h1

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	-	-2	2	-1	-	-5	4	-5	7	-2	-	-6	3	9	-15	7	-2	-3	-11	0	-6	-15	-7

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Quadratic twists for elliptic curve 6970h1

-4	-3	5	17
55760ba1	62730h1	34850d1	118490n1

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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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