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	2548g	Isogeny class
Conductor	2548	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	216	Modular degree for the optimal curve
Δ	-163072 = -1 · 28 · 72 · 13	Discriminant
Eigenvalues	2-  2  0 7- -3 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,12,8]	[a1,a2,a3,a4,a6]
Generators	[2:6:1]	Generators of the group modulo torsion
j	14000/13	j-invariant
L	4.1697093333486	L(r)(E,1)/r!
Ω	2.1137964076317	Real period
R	0.65753878003484	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10192z1 40768bt1 22932l1 63700ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2548g1

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
-	2	0	-	-3	+	-3	-5	0	-9	-8	2	6	8	9	-3	-9	7	5	3	-2	-10	12	-6	16

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Quadratic twists for elliptic curve 2548g1

-4	8	-3	5	-7	13
10192z1	40768bt1	22932l1	63700ba1	2548d1	33124o1

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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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