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	1248g	Isogeny class
Conductor	1248	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	7488 = 26 · 32 · 13	Discriminant
Eigenvalues	2- 3+  0 -2  0 13-  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-18,36]	[a1,a2,a3,a4,a6]
Generators	[0:6:1]	Generators of the group modulo torsion
j	10648000/117	j-invariant
L	2.2345904024442	L(r)(E,1)/r!
Ω	4.1927736527158	Real period
R	0.53296232697817	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	1248j1 2496z2 3744f1 31200o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1248g1

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	0	-	2	2	-8	6	-2	-6	0	-4	-8	-6	-4	2	-2	-4	-2	-12	12	12	-18

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Quadratic twists for elliptic curve 1248g1

-4	8	-3	5	-7	13
1248j1	2496z2	3744f1	31200o1	61152br1	16224b1

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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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