Cremona's table of elliptic curves

1001 = 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	7+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	1001a	Isogeny class
Conductor	1001	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1680	Modular degree for the optimal curve
Δ	-1864582578859 = -1 · 73 · 114 · 135	Discriminant
Eigenvalues	0  2 -1 7+ 11+ 13+  2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-15881,778423]	[a1,a2,a3,a4,a6]
Generators	[61:181:1]	Generators of the group modulo torsion
j	-442980486619070464/1864582578859	j-invariant
L	2.6180409634739	L(r)(E,1)/r!
Ω	0.837832406993	Real period
R	1.5623894120246	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	16016l1 64064j1 9009g1 25025g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1001a1

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 1001a1

-4	8	-3	5	-7	-11	13
16016l1	64064j1	9009g1	25025g1	7007b1	11011n1	13013q1

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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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