Cremona's table of elliptic curves

555 = 3 · 5 · 37

Field	Data	Notes
Atkin-Lehner	3- 5+ 37+	Signs for the Atkin-Lehner involutions
Class	555a	Isogeny class
Conductor	555	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	60	Modular degree for the optimal curve
Δ	-346875 = -1 · 3 · 55 · 37	Discriminant
Eigenvalues	0 3- 5+ -2  4  5 -2  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1,-29]	[a1,a2,a3,a4,a6]
j	-262144/346875	j-invariant
L	1.3704794284217	L(r)(E,1)/r!
Ω	1.3704794284217	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	8880k1 35520r1 1665e1 2775c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 555a1

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
0	-	+	-2	4	5	-2	6	6	3	-6	+	0	-11	9	3	-1	-2	-8	12	6	12	-1	1	2

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Quadratic twists for elliptic curve 555a1

-4	8	-3	5	-7	-11	13	37
8880k1	35520r1	1665e1	2775c1	27195h1	67155g1	93795x1	20535e1

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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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