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
Δ	6620155222590000 = 24 · 316 · 54 · 7 · 133	Discriminant
Eigenvalues	2+ 3+ 5+ 7+ -4 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1315758,-581449788]	[a1,a2,a3,a4,a6]
Generators	[2641:118567:1]	Generators of the group modulo torsion
j	251913989442882736925929/6620155222590000	j-invariant
L	1.8306492028308	L(r)(E,1)/r!
Ω	0.14096334333214	Real period
R	6.4933519578828	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	21840bw4 87360db4 8190bn3 13650cv3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730a3

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 2730a3

-4	8	-3	5	-7	13
21840bw4	87360db4	8190bn3	13650cv3	19110bl3	35490cs4

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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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