Cremona's table of elliptic curves

1488 = 2⁴ · 3 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 31-	Signs for the Atkin-Lehner involutions
Class	1488g	Isogeny class
Conductor	1488	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-1714176 = -1 · 211 · 33 · 31	Discriminant
Eigenvalues	2+ 3- -3 -2  5  1  1 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-32,84]	[a1,a2,a3,a4,a6]
Generators	[-2:12:1]	Generators of the group modulo torsion
j	-1825346/837	j-invariant
L	2.7761217283214	L(r)(E,1)/r!
Ω	2.4809875789948	Real period
R	0.093246527841888	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	744e1 5952y1 4464k1 37200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1488g1

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
+	-	-3	-2	5	1	1	-7	-8	-4	-	2	6	-10	-9	6	-10	-7	-5	-5	-6	-5	15	6	-19

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Quadratic twists for elliptic curve 1488g1

-4	8	-3	5	-7	-31
744e1	5952y1	4464k1	37200e1	72912g1	46128i1

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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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