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	1001b	Isogeny class
Conductor	1001	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	62811265517 = 7 · 11 · 138	Discriminant
Eigenvalues	-1  0 -2 7+ 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1006,2552]	[a1,a2,a3,a4,a6]
j	112489728522417/62811265517	j-invariant
L	0.47843048872809	L(r)(E,1)/r!
Ω	0.95686097745618	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16016j3 64064a3 9009c3 25025k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1001b4

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	0	-2	+	-	+	-2	-4	0	6	-4	6	6	12	4	-10	0	10	12	0	14	0	-4	-14	-14

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Quadratic twists for elliptic curve 1001b4

-4	8	-3	5	-7	-11	13
16016j3	64064a3	9009c3	25025k3	7007c3	11011p3	13013i4

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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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