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	2730bd	Isogeny class
Conductor	2730	Conductor
∏ cp	864	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	11650189824000 = 212 · 36 · 53 · 74 · 13	Discriminant
Eigenvalues	2- 3- 5- 7-  0 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-25725,1577457]	[a1,a2,a3,a4,a6]
j	1882742462388824401/11650189824000	j-invariant
L	4.3171915696536	L(r)(E,1)/r!
Ω	0.7195319282756	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	12	Number of elements in the torsion subgroup
Twists	21840bk1 87360m1 8190m1 13650a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730bd1

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	-	6	-4	0	6	-4	-10	6	8	0	-6	-12	14	-4	0	2	8	-12	6	2

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Quadratic twists for elliptic curve 2730bd1

-4	8	-3	5	-7	13
21840bk1	87360m1	8190m1	13650a1	19110bo1	35490x1

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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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