Cremona's table of elliptic curves

1349 = 19 · 71

Field	Data	Notes
Atkin-Lehner	19+ 71+	Signs for the Atkin-Lehner involutions
Class	1349a	Isogeny class
Conductor	1349	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-95779 = -1 · 19 · 712	Discriminant
Eigenvalues	0  0 -1  1  1  6 -1 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-8,17]	[a1,a2,a3,a4,a6]
Generators	[11:35:1]	Generators of the group modulo torsion
j	-56623104/95779	j-invariant
L	2.2402944680548	L(r)(E,1)/r!
Ω	3.0224948770616	Real period
R	0.37060351781848	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	21584d1 86336e1 12141e1 33725a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1349a1

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	0	-1	1	1	6	-1	+	0	4	-8	-6	-10	-1	-9	0	10	1	-8	+	-3	-10	12	-4	8

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Quadratic twists for elliptic curve 1349a1

-4	8	-3	5	-7	-19	-71
21584d1	86336e1	12141e1	33725a1	66101f1	25631e1	95779a1

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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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