Cremona's table of elliptic curves

7007 = 7² · 11 · 13

Field	Data	Notes
Atkin-Lehner	7- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	7007b	Isogeny class
Conductor	7007	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-219366275820182491 = -1 · 79 · 114 · 135	Discriminant
Eigenvalues	0 -2  1 7- 11+ 13- -2  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-778185,-265442817]	[a1,a2,a3,a4,a6]
Generators	[6351:501000:1]	Generators of the group modulo torsion
j	-442980486619070464/1864582578859	j-invariant
L	2.2688771911735	L(r)(E,1)/r!
Ω	0.080350652610161	Real period
R	1.4118598402563	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	112112bu1 63063x1 1001a1 77077j1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7007b1

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
0	-2	1	-	+	-	-2	1	-5	-5	9	10	2	-13	7	-1	-8	2	2	6	-5	11	3	-5	-5

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Quadratic twists for elliptic curve 7007b1

-4	-3	-7	-11	13
112112bu1	63063x1	1001a1	77077j1	91091n1

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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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