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	8	Product of Tamagawa factors cp
deg	152	Modular degree for the optimal curve
Δ	-17320303 = -1 · 7 · 114 · 132	Discriminant
Eigenvalues	-1  0 -2 7+ 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-16,-198]	[a1,a2,a3,a4,a6]
j	-426957777/17320303	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	4	Number of elements in the torsion subgroup
Twists	16016j1 64064a1 9009c1 25025k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1001b1

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 1001b1

-4	8	-3	5	-7	-11	13
16016j1	64064a1	9009c1	25025k1	7007c1	11011p1	13013i1

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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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