Cremona's table of elliptic curves

369 = 3² · 41

Field	Data	Notes
Atkin-Lehner	3- 41-	Signs for the Atkin-Lehner involutions
Class	369a	Isogeny class
Conductor	369	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-89667 = -1 · 37 · 41	Discriminant
Eigenvalues	0 3-  2 -4 -5 -4  5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,6,13]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	32768/123	j-invariant
L	1.5724499827809	L(r)(E,1)/r!
Ω	2.4151226244498	Real period
R	0.3255424728463	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	5904t1 23616v1 123b1 9225w1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 369a1

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	-4	-5	-4	5	-2	-4	-1	-5	-7	-	7	-7	14	12	-3	-2	3	13	-2	2	-18	-14

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Quadratic twists for elliptic curve 369a1

-4	8	-3	5	-7	-11	13	17	41
5904t1	23616v1	123b1	9225w1	18081h1	44649g1	62361e1	106641a1	15129c1

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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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