Cremona's table of elliptic curves

1248 = 2⁵ · 3 · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 13-	Signs for the Atkin-Lehner involutions
Class	1248h	Isogeny class
Conductor	1248	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	7884864 = 26 · 36 · 132	Discriminant
Eigenvalues	2- 3+ -2  0  4 13- -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-234,-1296]	[a1,a2,a3,a4,a6]
Generators	[234:3564:1]	Generators of the group modulo torsion
j	22235451328/123201	j-invariant
L	2.1339749893058	L(r)(E,1)/r!
Ω	1.2206352993933	Real period
R	3.4964988975274	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1248e1 2496h2 3744h1 31200n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1248h1

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	4	-	-6	-8	8	2	8	-10	6	-4	0	-14	-12	-10	-8	0	-14	-4	4	-10	10

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Quadratic twists for elliptic curve 1248h1

-4	8	-3	5	-7	13
1248e1	2496h2	3744h1	31200n1	61152bt1	16224c1

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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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