Cremona's table of elliptic curves

361 = 19²

Field	Data	Notes
Atkin-Lehner	19-	Signs for the Atkin-Lehner involutions
Class	361b	Isogeny class
Conductor	361	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-893871739 = -1 · 197	Discriminant
Eigenvalues	0  2  3 -1  3  4 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,241,-17]	[a1,a2,a3,a4,a6]
j	32768/19	j-invariant
L	1.8936398595948	L(r)(E,1)/r!
Ω	0.94681992979742	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5776q1 23104u1 3249c1 9025c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 361b1

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	2	3	-1	3	4	-3	-	0	-6	4	-2	6	-1	-3	-12	6	-1	4	-6	-7	-8	12	-12	-8

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Quadratic twists for elliptic curve 361b1

-4	8	-3	5	-7	-11	13	17	-19
5776q1	23104u1	3249c1	9025c1	17689g1	43681j1	61009b1	104329b1	19a3

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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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