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	2730v	Isogeny class
Conductor	2730	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	1098974822400 = 216 · 34 · 52 · 72 · 132	Discriminant
Eigenvalues	2- 3+ 5- 7+  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-349440,79361697]	[a1,a2,a3,a4,a6]
j	4718909406724749250561/1098974822400	j-invariant
L	2.7727274484007	L(r)(E,1)/r!
Ω	0.69318186210018	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	21840cl2 87360bx2 8190l2 13650bd2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730v2

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

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Quadratic twists for elliptic curve 2730v2

-4	8	-3	5	-7	13
21840cl2	87360bx2	8190l2	13650bd2	19110cm2	35490k2

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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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