Cremona's table of elliptic curves

2730 = 2 · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	2730s	Isogeny class
Conductor	2730	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-1552332600 = -1 · 23 · 38 · 52 · 7 · 132	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -2 13-  0  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,189,1689]	[a1,a2,a3,a4,a6]
Generators	[9:60:1]	Generators of the group modulo torsion
j	746389464911/1552332600	j-invariant
L	3.8095340498578	L(r)(E,1)/r!
Ω	1.0421107799711	Real period
R	0.60926568829907	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	21840bz2 87360cu2 8190r2 13650bc2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730s2

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	-	0	4	-4	-10	2	2	-8	-2	0	4	4	-10	-8	-8	-6	-8	4	-16	-2

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Quadratic twists for elliptic curve 2730s2

-4	8	-3	5	-7	13
21840bz2	87360cu2	8190r2	13650bc2	19110cz2	35490r2

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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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