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	55488de	Isogeny class
Conductor	55488	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	-9236754432 = -1 · 212 · 33 · 174	Discriminant
Eigenvalues	2- 3+  2 -5  2  1 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2697,55017]	[a1,a2,a3,a4,a6]
Generators	[23:68:1]	Generators of the group modulo torsion
j	-6344128/27	j-invariant
L	4.80133071347	L(r)(E,1)/r!
Ω	1.3039406087775	Real period
R	0.6136949644658	Regulator
r	1	Rank of the group of rational points
S	1.0000000000114	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	55488eg1 27744bd1 55488dw1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 55488de1

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	-5	2	1	-	-1	-4	2	1	11	-2	5	-6	0	4	7	-5	-10	6	0	-4	-12	-11

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Quadratic twists for elliptic curve 55488de1

-4	8	17
55488eg1	27744bd1	55488dw1

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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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