Cremona's table of elliptic curves

6732 = 2² · 3² · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 11- 17-	Signs for the Atkin-Lehner involutions
Class	6732a	Isogeny class
Conductor	6732	Conductor
∏ cp	54	Product of Tamagawa factors cp
Δ	-98850149874432 = -1 · 28 · 310 · 113 · 173	Discriminant
Eigenvalues	2- 3-  0 -1 11- -4 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-292440,60871876]	[a1,a2,a3,a4,a6]
Generators	[-448:10098:1]	Generators of the group modulo torsion
j	-14820625871872000/529675443	j-invariant
L	3.9458764917555	L(r)(E,1)/r!
Ω	0.56027200218259	Real period
R	1.1737978685305	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	26928bg2 107712bd2 2244b2 74052e2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6732a2

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	-1	-	-4	-	2	6	-3	-4	2	9	2	3	-9	9	2	-7	-6	-13	8	-6	3	-10

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Quadratic twists for elliptic curve 6732a2

-4	8	-3	-11	17
26928bg2	107712bd2	2244b2	74052e2	114444a2

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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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