Cremona's table of elliptic curves

364 = 2² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 7- 13+	Signs for the Atkin-Lehner involutions
Class	364a	Isogeny class
Conductor	364	Conductor
∏ cp	15	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-55933696 = -1 · 28 · 75 · 13	Discriminant
Eigenvalues	2-  0 -3 7- -2 13+ -4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-584,5444]	[a1,a2,a3,a4,a6]
Generators	[-8:98:1]	Generators of the group modulo torsion
j	-86044336128/218491	j-invariant
L	1.5755626643576	L(r)(E,1)/r!
Ω	1.9913710109388	Real period
R	0.052746329227547	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	1456e1 5824k1 3276k1 9100d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 364a1

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	-3	-	-2	+	-4	-1	-7	7	-5	4	-6	9	-7	11	0	-2	-10	0	7	1	-11	-1	-13

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Quadratic twists for elliptic curve 364a1

-4	8	-3	5	-7	-11	13	17
1456e1	5824k1	3276k1	9100d1	2548j1	44044g1	4732b1	105196a1

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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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