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	6970g	Isogeny class
Conductor	6970	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	20416	Modular degree for the optimal curve
Δ	-491908474880 = -1 · 211 · 5 · 17 · 414	Discriminant
Eigenvalues	2-  3 5-  2  0  7 17- -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1332,-38249]	[a1,a2,a3,a4,a6]
j	-261174445778961/491908474880	j-invariant
L	8.186827785753	L(r)(E,1)/r!
Ω	0.37212853571605	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	55760y1 62730i1 34850c1 118490q1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 6970g1

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
-	3	-	2	0	7	-	-5	-6	3	-1	-8	+	-6	5	-3	-5	1	10	-9	-3	-16	4	3	3

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Quadratic twists for elliptic curve 6970g1

-4	-3	5	17
55760y1	62730i1	34850c1	118490q1

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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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