Cremona's table of elliptic curves

27552 = 2⁵ · 3 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 41-	Signs for the Atkin-Lehner involutions
Class	27552q	Isogeny class
Conductor	27552	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	47444544 = 26 · 32 · 72 · 412	Discriminant
Eigenvalues	2- 3+ -2 7+  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-574,-5096]	[a1,a2,a3,a4,a6]
Generators	[36:140:1]	Generators of the group modulo torsion
j	327367684288/741321	j-invariant
L	3.4677610484283	L(r)(E,1)/r!
Ω	0.97536606407417	Real period
R	3.5553431436227	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	27552bc1 55104da2 82656i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 27552q1

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	+	4	-2	-6	4	-4	6	-4	6	-	0	-8	6	0	-2	-4	0	10	8	0	18	-10

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Quadratic twists for elliptic curve 27552q1

-4	8	-3
27552bc1	55104da2	82656i1

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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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