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	1248d	Isogeny class
Conductor	1248	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	320	Modular degree for the optimal curve
Δ	49128768 = 26 · 310 · 13	Discriminant
Eigenvalues	2+ 3-  0 -2 -4 13- -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-98,132]	[a1,a2,a3,a4,a6]
Generators	[-2:18:1]	Generators of the group modulo torsion
j	1643032000/767637	j-invariant
L	2.8732043345733	L(r)(E,1)/r!
Ω	1.7940718838874	Real period
R	0.32029980073571	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1248b1 2496r2 3744n1 31200bg1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1248d1

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

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Quadratic twists for elliptic curve 1248d1

-4	8	-3	5	-7	13
1248b1	2496r2	3744n1	31200bg1	61152b1	16224s1

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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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