Cremona's table of elliptic curves

248 = 2³ · 31

Field	Data	Notes
Atkin-Lehner	2+ 31+	Signs for the Atkin-Lehner involutions
Class	248a	Isogeny class
Conductor	248	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-496 = -1 · 24 · 31	Discriminant
Eigenvalues	2+ -2  1 -3 -2 -2 -6  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,0,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-256/31	j-invariant
L	1.2011105982982	L(r)(E,1)/r!
Ω	4.293793650815	Real period
R	0.13986589668442	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	496b1 1984c1 2232j1 6200i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 248a1

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	1	-3	-2	-2	-6	1	-6	4	+	-2	7	4	8	8	3	-6	-12	3	-10	-12	2	-16	-7

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Quadratic twists for elliptic curve 248a1

-4	8	-3	5	-7	-11	13	17	-19	-31
496b1	1984c1	2232j1	6200i1	12152c1	30008g1	41912i1	71672d1	89528h1	7688c1

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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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