Cremona's table of elliptic curves

1311 = 3 · 19 · 23

Field	Data	Notes
Atkin-Lehner	3+ 19+ 23-	Signs for the Atkin-Lehner involutions
Class	1311a	Isogeny class
Conductor	1311	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	780	Modular degree for the optimal curve
Δ	271377 = 33 · 19 · 232	Discriminant
Eigenvalues	-1 3+ -2  0 -4 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5654,161282]	[a1,a2,a3,a4,a6]
j	19989223566735457/271377	j-invariant
L	0.27407827464521	L(r)(E,1)/r!
Ω	2.1926261971617	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	20976j1 83904p1 3933a1 32775t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1311a1

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	+	-2	0	-4	-2	-6	+	-	-2	8	-2	-6	-12	0	6	4	14	12	0	10	8	-12	-6	10

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Quadratic twists for elliptic curve 1311a1

-4	8	-3	5	-7	-19	-23
20976j1	83904p1	3933a1	32775t1	64239o1	24909m1	30153c1

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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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