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	2730j	Isogeny class
Conductor	2730	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	960	Modular degree for the optimal curve
Δ	91990080 = 26 · 35 · 5 · 7 · 132	Discriminant
Eigenvalues	2+ 3+ 5- 7-  2 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-142,-524]	[a1,a2,a3,a4,a6]
j	320153881321/91990080	j-invariant
L	1.4120246116759	L(r)(E,1)/r!
Ω	1.4120246116759	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	21840cf1 87360cg1 8190bk1 13650cl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730j1

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	2	4	-4	0	-2	-6	0	8	10	-8	4	2	8	-14	-8	14	-6	6

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Quadratic twists for elliptic curve 2730j1

-4	8	-3	5	-7	13
21840cf1	87360cg1	8190bk1	13650cl1	19110v1	35490cd1

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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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