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	1309b	Isogeny class
Conductor	1309	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-155771 = -1 · 72 · 11 · 172	Discriminant
Eigenvalues	-2 -1 -3 7+ 11+ -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-22,52]	[a1,a2,a3,a4,a6]
Generators	[-5:3:1] [-1:8:1]	Generators of the group modulo torsion
j	-1231925248/155771	j-invariant
L	1.3361816137231	L(r)(E,1)/r!
Ω	3.1455350713333	Real period
R	0.10619668700399	Regulator
r	2	Rank of the group of rational points
S	1.0000000000009	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20944o1 83776i1 11781e1 32725f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1309b1

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	-1	-3	+	+	-6	-	-4	-3	-4	-9	-3	-10	-4	-12	2	11	6	-11	15	-4	-12	-16	1	-7

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Quadratic twists for elliptic curve 1309b1

-4	8	-3	5	-7	-11	17
20944o1	83776i1	11781e1	32725f1	9163e1	14399d1	22253l1

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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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