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	1248c	Isogeny class
Conductor	1248	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	922529088 = 26 · 38 · 133	Discriminant
Eigenvalues	2+ 3-  2  2 -2 13+  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2902,-61132]	[a1,a2,a3,a4,a6]
j	42246001231552/14414517	j-invariant
L	2.6018461727784	L(r)(E,1)/r!
Ω	0.65046154319461	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	1248f1 2496f2 3744l1 31200bp1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1248c1

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 1248c1

-4	8	-3	5	-7	13
1248f1	2496f2	3744l1	31200bp1	61152l1	16224u1

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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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