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	1309c	Isogeny class
Conductor	1309	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-7761061 = -1 · 73 · 113 · 17	Discriminant
Eigenvalues	-1  0  1 7+ 11-  1 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-142,698]	[a1,a2,a3,a4,a6]
Generators	[8:-10:1]	Generators of the group modulo torsion
j	-314570740401/7761061	j-invariant
L	1.7893099436714	L(r)(E,1)/r!
Ω	2.3372327997925	Real period
R	0.25518923401358	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	20944i1 83776c1 11781c1 32725j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1309c1

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	1	+	-	1	-	-4	7	-3	-2	4	12	-11	-12	-9	3	-4	-8	5	-6	6	2	-14	-10

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Quadratic twists for elliptic curve 1309c1

-4	8	-3	5	-7	-11	17
20944i1	83776c1	11781c1	32725j1	9163f1	14399c1	22253g1

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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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