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	16	Product of Tamagawa factors cp
Δ	3158618112 = 212 · 33 · 134	Discriminant
Eigenvalues	2- 3+ -2  0  4 13- -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-369,513]	[a1,a2,a3,a4,a6]
Generators	[1:12:1]	Generators of the group modulo torsion
j	1360251712/771147	j-invariant
L	2.1339749893058	L(r)(E,1)/r!
Ω	1.2206352993933	Real period
R	1.7482494487637	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	1248e2 2496h1 3744h2 31200n3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1248h3

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 1248h3

-4	8	-3	5	-7	13
1248e2	2496h1	3744h2	31200n3	61152bt3	16224c3

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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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