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	555b	Isogeny class
Conductor	555	Conductor
∏ cp	45	Product of Tamagawa factors cp
deg	420	Modular degree for the optimal curve
Δ	-66363694875 = -1 · 315 · 53 · 37	Discriminant
Eigenvalues	0 3- 5-  2  0 -1  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2405,-47869]	[a1,a2,a3,a4,a6]
j	-1539038632738816/66363694875	j-invariant
L	1.7000104938638	L(r)(E,1)/r!
Ω	0.34000209877276	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	8880r1 35520b1 1665c1 2775a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 555b1

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	0	-1	6	2	-6	9	2	-	0	-1	9	3	-3	-10	-4	0	-10	-4	-9	3	-10

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Quadratic twists for elliptic curve 555b1

-4	8	-3	5	-7	-11	13	37
8880r1	35520b1	1665c1	2775a1	27195d1	67155s1	93795n1	20535b1

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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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