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	1488d	Isogeny class
Conductor	1488	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-38609136 = -1 · 24 · 34 · 313	Discriminant
Eigenvalues	2+ 3-  1  3  2  4 -4  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-140,-753]	[a1,a2,a3,a4,a6]
j	-19102326016/2413071	j-invariant
L	2.7547559223789	L(r)(E,1)/r!
Ω	0.68868898059472	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	744f1 5952w1 4464c1 37200a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1488d1

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
+	-	1	3	2	4	-4	7	-4	-6	+	-6	3	2	12	4	-7	-8	4	1	-2	14	-14	-6	-7

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Quadratic twists for elliptic curve 1488d1

-4	8	-3	5	-7	-31
744f1	5952w1	4464c1	37200a1	72912n1	46128c1

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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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