Cremona's table of elliptic curves

1309 = 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	7+ 11+ 17-	Signs for the Atkin-Lehner involutions
Class	1309a	Isogeny class
Conductor	1309	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16128	Modular degree for the optimal curve
Δ	-45254746691 = -1 · 76 · 113 · 172	Discriminant
Eigenvalues	2  3  1 7+ 11+ -2 17-  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-406957,-99924251]	[a1,a2,a3,a4,a6]
j	-7453654902730081529856/45254746691	j-invariant
L	6.0487049709618	L(r)(E,1)/r!
Ω	0.094511015171277	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20944p1 83776j1 11781f1 32725g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1309a1

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
2	3	1	+	+	-2	-	8	1	0	-5	1	6	4	-12	-6	3	-10	-11	-13	0	0	8	1	5

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Quadratic twists for elliptic curve 1309a1

-4	8	-3	5	-7	-11	17
20944p1	83776j1	11781f1	32725g1	9163d1	14399e1	22253k1

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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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