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	2730a	Isogeny class
Conductor	2730	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	140009392373760 = 216 · 34 · 5 · 74 · 133	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-22718,1179252]	[a1,a2,a3,a4,a6]
Generators	[-148:1226:1]	Generators of the group modulo torsion
j	1296772724742600169/140009392373760	j-invariant
L	1.8306492028308	L(r)(E,1)/r!
Ω	0.56385337332854	Real period
R	1.6233379894707	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	21840bw1 87360db1 8190bn1 13650cv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730a1

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

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Quadratic twists for elliptic curve 2730a1

-4	8	-3	5	-7	13
21840bw1	87360db1	8190bn1	13650cv1	19110bl1	35490cs1

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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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