Cremona's table of elliptic curves

455 = 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	455a	Isogeny class
Conductor	455	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	3901625 = 53 · 74 · 13	Discriminant
Eigenvalues	1  0 5+ 7+  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-50,111]	[a1,a2,a3,a4,a6]
Generators	[2:3:1]	Generators of the group modulo torsion
j	13980103929/3901625	j-invariant
L	2.1253916593497	L(r)(E,1)/r!
Ω	2.3100747042975	Real period
R	1.8401064306672	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	7280q1 29120r1 4095j1 2275d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 455a1

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	+	+	0	+	-2	-4	0	-2	0	2	6	-4	-8	6	-4	-10	12	4	-10	0	12	-18	-2

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Quadratic twists for elliptic curve 455a1

-4	8	-3	5	-7	-11	13
7280q1	29120r1	4095j1	2275d1	3185h1	55055h1	5915k1

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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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