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	1248f	Isogeny class
Conductor	1248	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1601419382784 = -1 · 212 · 34 · 136	Discriminant
Eigenvalues	2- 3+  2 -2  2 13+  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2497,78385]	[a1,a2,a3,a4,a6]
j	-420526439488/390971529	j-invariant
L	1.5415298120343	L(r)(E,1)/r!
Ω	0.77076490601717	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1248c2 2496o1 3744d2 31200w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1248f2

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

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Quadratic twists for elliptic curve 1248f2

-4	8	-3	5	-7	13
1248c2	2496o1	3744d2	31200w2	61152cd2	16224d2

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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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