Cremona's table of elliptic curves

6710 = 2 · 5 · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 5- 11- 61-	Signs for the Atkin-Lehner involutions
Class	6710h	Isogeny class
Conductor	6710	Conductor
∏ cp	90	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	125748620800 = 29 · 52 · 115 · 61	Discriminant
Eigenvalues	2-  1 5- -2 11-  1 -3 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1255,1225]	[a1,a2,a3,a4,a6]
Generators	[-30:125:1]	Generators of the group modulo torsion
j	218613268577521/125748620800	j-invariant
L	6.9187927144488	L(r)(E,1)/r!
Ω	0.89048784996761	Real period
R	0.086329616521757	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53680bc1 60390h1 33550g1 73810e1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6710h1

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	-	1	-3	-2	-8	-6	7	-3	2	-1	2	3	-2	-	-14	-15	-4	-10	14	-6	5

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Quadratic twists for elliptic curve 6710h1

-4	-3	5	-11
53680bc1	60390h1	33550g1	73810e1

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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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