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	2730h	Isogeny class
Conductor	2730	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-589680 = -1 · 24 · 34 · 5 · 7 · 13	Discriminant
Eigenvalues	2+ 3+ 5- 7-  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,36]	[a1,a2,a3,a4,a6]
Generators	[0:6:1]	Generators of the group modulo torsion
j	-1771561/589680	j-invariant
L	2.2874764991882	L(r)(E,1)/r!
Ω	2.3586037683917	Real period
R	0.969843485304	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	21840cc1 87360cp1 8190bh1 13650cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730h1

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	-4	4	-2	0	-6	-6	0	-12	-10	-4	10	4	0	2	16	-12	18	2

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Quadratic twists for elliptic curve 2730h1

-4	8	-3	5	-7	13
21840cc1	87360cp1	8190bh1	13650cn1	19110w1	35490bz1

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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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