Cremona's table of elliptic curves

720 = 2⁴ · 3² · 5

Field	Data	Notes
Atkin-Lehner	2- 3+ 5-	Signs for the Atkin-Lehner involutions
Class	720g	Isogeny class
Conductor	720	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-25798901760 = -1 · 218 · 39 · 5	Discriminant
Eigenvalues	2- 3+ 5- -2 -6 -4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1107,16146]	[a1,a2,a3,a4,a6]
Generators	[15:54:1]	Generators of the group modulo torsion
j	-1860867/320	j-invariant
L	2.1771249053466	L(r)(E,1)/r!
Ω	1.1463561695731	Real period
R	0.94958485117121	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	90a3 2880v3 720f1 3600ba3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 720g3

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
-	+	-	-2	-6	-4	-6	4	0	-6	4	8	0	-8	0	-6	-6	2	4	12	-10	4	-12	12	2

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Quadratic twists for elliptic curve 720g3

-4	8	-3	5	-7	-11	13
90a3	2880v3	720f1	3600ba3	35280df3	87120dl3	121680ck3

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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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