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	2730i	Isogeny class
Conductor	2730	Conductor
∏ cp	280	Product of Tamagawa factors cp
deg	134400	Modular degree for the optimal curve
Δ	2.379571497576E+19	Discriminant
Eigenvalues	2+ 3+ 5- 7- -6 13+  4  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1534592,692407296]	[a1,a2,a3,a4,a6]
Generators	[527:5249:1]	Generators of the group modulo torsion
j	399671282266555297146121/23795714975760000000	j-invariant
L	2.2108226270988	L(r)(E,1)/r!
Ω	0.20981497290378	Real period
R	0.15052872514303	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	21840ce1 87360cs1 8190bj1 13650cq1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730i1

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

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Quadratic twists for elliptic curve 2730i1

-4	8	-3	5	-7	13
21840ce1	87360cs1	8190bj1	13650cq1	19110bc1	35490cf1

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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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