Cremona's table of elliptic curves

1457 = 31 · 47

Field	Data	Notes
Atkin-Lehner	31- 47+	Signs for the Atkin-Lehner involutions
Class	1457a	Isogeny class
Conductor	1457	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	160	Modular degree for the optimal curve
Δ	2122849 = 312 · 472	Discriminant
Eigenvalues	-1  0 -2  0  4 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-36,-34]	[a1,a2,a3,a4,a6]
j	5026574097/2122849	j-invariant
L	0.50712038515032	L(r)(E,1)/r!
Ω	2.0284815406013	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	23312i2 93248j2 13113h2 36425f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1457a1

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	0	-2	0	4	-6	2	-4	0	-6	-	6	10	-4	+	6	-4	14	4	0	6	4	0	18	2

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Quadratic twists for elliptic curve 1457a1

-4	8	-3	5	-7	-31	-47
23312i2	93248j2	13113h2	36425f2	71393c2	45167c2	68479a2

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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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