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	16	Product of Tamagawa factors cp
Δ	73645476129 = 36 · 192 · 234	Discriminant
Eigenvalues	-1 3+ -2  0 -4 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5659,160976]	[a1,a2,a3,a4,a6]
j	20042301472793137/73645476129	j-invariant
L	0.27407827464521	L(r)(E,1)/r!
Ω	1.0963130985808	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	20976j2 83904p2 3933a2 32775t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1311a2

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 1311a2

-4	8	-3	5	-7	-19	-23
20976j2	83904p2	3933a2	32775t2	64239o2	24909m2	30153c2

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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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