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	2730d	Isogeny class
Conductor	2730	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	7156531200 = 220 · 3 · 52 · 7 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  4 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-483,-627]	[a1,a2,a3,a4,a6]
j	12501706118329/7156531200	j-invariant
L	1.1037692158881	L(r)(E,1)/r!
Ω	1.1037692158881	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	21840bq1 87360dr1 8190bs1 13650cp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730d1

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	+	2	4	4	2	-8	-6	10	-4	0	-6	8	10	-8	-16	14	-16	16	18	-10

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Quadratic twists for elliptic curve 2730d1

-4	8	-3	5	-7	13
21840bq1	87360dr1	8190bs1	13650cp1	19110bj1	35490co1

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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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