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	2730w	Isogeny class
Conductor	2730	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	5038160400 = 24 · 32 · 52 · 72 · 134	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4 13-  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-455,1325]	[a1,a2,a3,a4,a6]
j	10418796526321/5038160400	j-invariant
L	2.4286434708265	L(r)(E,1)/r!
Ω	1.2143217354132	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	21840ck2 87360bw2 8190k2 13650be2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730w2

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

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Quadratic twists for elliptic curve 2730w2

-4	8	-3	5	-7	13
21840ck2	87360bw2	8190k2	13650be2	19110co2	35490i2

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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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