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	2730l	Isogeny class
Conductor	2730	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	3478020 = 22 · 3 · 5 · 73 · 132	Discriminant
Eigenvalues	2+ 3- 5+ 7+  6 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-99,-374]	[a1,a2,a3,a4,a6]
j	105756712489/3478020	j-invariant
L	1.5184234890431	L(r)(E,1)/r!
Ω	1.5184234890431	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21840bj1 87360bd1 8190bo1 13650ca1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730l1

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
+	-	+	+	6	+	-2	-2	-4	8	4	2	6	12	-12	-14	0	-4	14	8	6	-8	2	-2	18

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Quadratic twists for elliptic curve 2730l1

-4	8	-3	5	-7	13
21840bj1	87360bd1	8190bo1	13650ca1	19110q1	35490dv1

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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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