Cremona's table of elliptic curves

48608 = 2⁵ · 7² · 31

Field	Data	Notes
Atkin-Lehner	2+ 7- 31+	Signs for the Atkin-Lehner involutions
Class	48608c	Isogeny class
Conductor	48608	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	-640492450304 = -1 · 29 · 79 · 31	Discriminant
Eigenvalues	2+ -1 -1 7-  0  0  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1976,-50588]	[a1,a2,a3,a4,a6]
Generators	[56:106:1] [89:686:1]	Generators of the group modulo torsion
j	-14172488/10633	j-invariant
L	7.5523614048839	L(r)(E,1)/r!
Ω	0.34670930452474	Real period
R	2.7228723408638	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	48608i1 97216g1 6944c1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 48608c1

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	-	0	0	2	-6	-1	-9	+	-6	0	-10	9	-2	8	-8	-11	12	-5	-11	-15	-1	4

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Quadratic twists for elliptic curve 48608c1

-4	8	-7
48608i1	97216g1	6944c1

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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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