Cremona's table of elliptic curves

6248 = 2³ · 11 · 71

Field	Data	Notes
Atkin-Lehner	2+ 11- 71+	Signs for the Atkin-Lehner involutions
Class	6248b	Isogeny class
Conductor	6248	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2592	Modular degree for the optimal curve
Δ	199936 = 28 · 11 · 71	Discriminant
Eigenvalues	2+  0  3 -1 11- -5  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4876,-131052]	[a1,a2,a3,a4,a6]
j	50081212818432/781	j-invariant
L	2.2853021182247	L(r)(E,1)/r!
Ω	0.57132552955619	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12496a1 49984b1 56232n1 68728d1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6248b1

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	3	-1	-	-5	3	6	0	8	2	5	5	-10	-2	0	0	-7	0	+	4	-10	14	9	6

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Quadratic twists for elliptic curve 6248b1

-4	8	-3	-11
12496a1	49984b1	56232n1	68728d1

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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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