Cremona's table of elliptic curves

55488 = 2⁶ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 17-	Signs for the Atkin-Lehner involutions
Class	55488dg	Isogeny class
Conductor	55488	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	156672	Modular degree for the optimal curve
Δ	-85718107435008 = -1 · 212 · 3 · 178	Discriminant
Eigenvalues	2- 3+ -2  3  2  5 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,6551,-398135]	[a1,a2,a3,a4,a6]
Generators	[130053:1436804:1331]	Generators of the group modulo torsion
j	1088/3	j-invariant
L	5.7079949409053	L(r)(E,1)/r!
Ω	0.31152314232312	Real period
R	9.1614300278493	Regulator
r	1	Rank of the group of rational points
S	1.0000000000013	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	55488eh1 27744bc1 55488dt1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 55488dg1

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
-	+	-2	3	2	5	-	3	-4	-6	9	7	-2	1	-2	-8	0	-13	7	2	6	16	-12	0	13

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Quadratic twists for elliptic curve 55488dg1

-4	8	17
55488eh1	27744bc1	55488dt1

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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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