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	1	Product of Tamagawa factors cp
Δ	1457 = 31 · 47	Discriminant
Eigenvalues	-1  0 -2  0  4 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-31,-58]	[a1,a2,a3,a4,a6]
j	3196010817/1457	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	2	Number of elements in the torsion subgroup
Twists	23312i1 93248j1 13113h1 36425f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1457a2

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 1457a2

-4	8	-3	5	-7	-31	-47
23312i1	93248j1	13113h1	36425f1	71393c1	45167c1	68479a1

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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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