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	2548b	Isogeny class
Conductor	2548	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	2016	Modular degree for the optimal curve
Δ	15588021904 = 24 · 78 · 132	Discriminant
Eigenvalues	2-  1  1 7+ -1 13- -5 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4230,-107143]	[a1,a2,a3,a4,a6]
Generators	[-38:13:1]	Generators of the group modulo torsion
j	90770176/169	j-invariant
L	3.7946849739284	L(r)(E,1)/r!
Ω	0.59204467586821	Real period
R	1.0682428563812	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	10192o1 40768b1 22932i1 63700b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2548b1

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
-	1	1	+	-1	-	-5	-7	-1	10	3	-11	-10	-8	9	-9	3	11	7	-8	-3	-1	-4	9	2

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Quadratic twists for elliptic curve 2548b1

-4	8	-3	5	-7	13
10192o1	40768b1	22932i1	63700b1	2548e1	33124a1

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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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