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	7007a	Isogeny class
Conductor	7007	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-218709491 = -1 · 76 · 11 · 132	Discriminant
Eigenvalues	0  1  1 7- 11+ 13-  4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-65,718]	[a1,a2,a3,a4,a6]
Generators	[2:24:1]	Generators of the group modulo torsion
j	-262144/1859	j-invariant
L	4.1587761985128	L(r)(E,1)/r!
Ω	1.5237806481968	Real period
R	0.68231214962503	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	112112bt1 63063y1 143a1 77077i1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7007a1

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	1	1	-	+	-	4	-2	7	-2	3	-11	-10	-4	4	2	1	2	-1	-9	16	8	0	7	13

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Quadratic twists for elliptic curve 7007a1

-4	-3	-7	-11	13
112112bt1	63063y1	143a1	77077i1	91091k1

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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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