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	-2345012441401743 = -1 · 324 · 192 · 23	Discriminant
Eigenvalues	-1 3+ -2  0 -4 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,33211,-24910]	[a1,a2,a3,a4,a6]
j	4051060719646926383/2345012441401743	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	20976j6 83904p5 3933a6 32775t5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1311a6

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 1311a6

-4	8	-3	5	-7	-19	-23
20976j6	83904p5	3933a6	32775t5	64239o5	24909m5	30153c5

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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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