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	4	Product of Tamagawa factors cp
Δ	284763401508447 = 36 · 198 · 23	Discriminant
Eigenvalues	-1 3+ -2  0 -4 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-92139,-10772718]	[a1,a2,a3,a4,a6]
j	86507645152456935217/284763401508447	j-invariant
L	0.27407827464521	L(r)(E,1)/r!
Ω	0.27407827464521	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	20976j5 83904p6 3933a5 32775t6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1311a5

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 1311a5

-4	8	-3	5	-7	-19	-23
20976j5	83904p6	3933a5	32775t6	64239o6	24909m6	30153c6

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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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