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	2730m	Isogeny class
Conductor	2730	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-3372408585000 = -1 · 23 · 32 · 54 · 78 · 13	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0 13+  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,3741,-6554]	[a1,a2,a3,a4,a6]
Generators	[14:213:1]	Generators of the group modulo torsion
j	5792335463322071/3372408585000	j-invariant
L	2.8097710657865	L(r)(E,1)/r!
Ω	0.46906544610545	Real period
R	0.74876839924882	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	21840y3 87360bo3 8190br4 13650bv4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730m4

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

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Quadratic twists for elliptic curve 2730m4

-4	8	-3	5	-7	13
21840y3	87360bo3	8190br4	13650bv4	19110o4	35490dk3

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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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