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	8	Product of Tamagawa factors cp
Δ	36637441034769 = 312 · 194 · 232	Discriminant
Eigenvalues	-1 3+ -2  0 -4 -2 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-8304,-8304]	[a1,a2,a3,a4,a6]
j	63327012793433857/36637441034769	j-invariant
L	0.27407827464521	L(r)(E,1)/r!
Ω	0.54815654929042	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	20976j3 83904p4 3933a3 32775t4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1311a3

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 1311a3

-4	8	-3	5	-7	-19	-23
20976j3	83904p4	3933a3	32775t4	64239o4	24909m4	30153c4

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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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