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	1311b	Isogeny class
Conductor	1311	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	-954885294459 = -1 · 36 · 195 · 232	Discriminant
Eigenvalues	0 3+ -1  1 -1  0  5 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1411,51723]	[a1,a2,a3,a4,a6]
Generators	[-11:256:1]	Generators of the group modulo torsion
j	-310894120566784/954885294459	j-invariant
L	1.92532584035	L(r)(E,1)/r!
Ω	0.77489858910963	Real period
R	0.12423082629188	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	20976g1 83904g1 3933c1 32775ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1311b1

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
0	+	-1	1	-1	0	5	-	-	0	-2	-10	-2	1	-9	2	-6	5	8	2	-7	-2	4	-4	-16

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Quadratic twists for elliptic curve 1311b1

-4	8	-3	5	-7	-19	-23
20976g1	83904g1	3933c1	32775ba1	64239k1	24909k1	30153a1

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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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