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	1311d	Isogeny class
Conductor	1311	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-293901291 = -1 · 34 · 193 · 232	Discriminant
Eigenvalues	-2 3- -3  1  1  0 -5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,18,830]	[a1,a2,a3,a4,a6]
Generators	[75:655:1]	Generators of the group modulo torsion
j	609800192/293901291	j-invariant
L	1.4850519280806	L(r)(E,1)/r!
Ω	1.3453478280137	Real period
R	0.045993431870612	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	20976f1 83904d1 3933f1 32775i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1311d1

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	-	-3	1	1	0	-5	-	+	-4	4	8	2	1	-3	0	-6	-3	-10	-16	1	4	-12	8	-16

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Quadratic twists for elliptic curve 1311d1

-4	8	-3	5	-7	-19	-23
20976f1	83904d1	3933f1	32775i1	64239d1	24909g1	30153g1

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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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