Cremona's table of elliptic curves

361 = 19²

Field	Data	Notes
Atkin-Lehner	19+	Signs for the Atkin-Lehner involutions
Class	361a	Isogeny class
Conductor	361	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-322687697779 = -1 · 199	Discriminant
Eigenvalues	0  0 -1  3 -5  0 -7 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-13718,-619025]	[a1,a2,a3,a4,a6]
Generators	[2527:126891:1]	Generators of the group modulo torsion
j	-884736	j-invariant
L	1.5194236564427	L(r)(E,1)/r!
Ω	0.22055526420031	Real period
R	3.4445418066802	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	5776g2 23104a2 3249a2 9025a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 361a2

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	3	-5	0	-7	+	-4	0	0	0	0	-1	13	0	0	15	0	0	-11	0	-16	0	0

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Quadratic twists for elliptic curve 361a2

-4	8	-3	5	-7	-11	13	17	-19
5776g2	23104a2	3249a2	9025a2	17689d2	43681h2	61009a2	104329a2	361a1

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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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