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	55488f	Isogeny class
Conductor	55488	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1216512	Modular degree for the optimal curve
Δ	-1190957300218773504 = -1 · 214 · 311 · 177	Discriminant
Eigenvalues	2+ 3+ -1 -4  3 -3 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1874261,-988397811]	[a1,a2,a3,a4,a6]
Generators	[34725780:679906891:19683]	Generators of the group modulo torsion
j	-1841198792704/3011499	j-invariant
L	2.8115027249998	L(r)(E,1)/r!
Ω	0.064508871755746	Real period
R	10.895798703558	Regulator
r	1	Rank of the group of rational points
S	1.0000000000082	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	55488dn1 3468f1 3264l1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 55488f1

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	-4	3	-3	+	-1	-3	-10	-6	-4	-5	1	-2	14	6	8	12	-12	-2	14	-6	16	0

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Quadratic twists for elliptic curve 55488f1

-4	8	17
55488dn1	3468f1	3264l1

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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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