Cremona's table of elliptic curves

2548 = 2² · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	2548a	Isogeny class
Conductor	2548	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	1008	Modular degree for the optimal curve
Δ	6492304 = 24 · 74 · 132	Discriminant
Eigenvalues	2- -3 -3 7+ -5 13+ -1 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-49,49]	[a1,a2,a3,a4,a6]
Generators	[-7:7:1] [-5:13:1]	Generators of the group modulo torsion
j	338688/169	j-invariant
L	2.3405439475191	L(r)(E,1)/r!
Ω	2.1047729265299	Real period
R	0.061778739961693	Regulator
r	2	Rank of the group of rational points
S	1.0000000000009	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10192n1 40768i1 22932g1 63700h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2548a1

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
-	-3	-3	+	-5	+	-1	-7	-1	-2	-5	-11	-6	-12	-7	11	3	-5	-1	0	-11	-5	4	5	2

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Quadratic twists for elliptic curve 2548a1

-4	8	-3	5	-7	13
10192n1	40768i1	22932g1	63700h1	2548k1	33124e1

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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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