Cremona's table of elliptic curves

68544 = 2⁶ · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 17-	Signs for the Atkin-Lehner involutions
Class	68544cp	Isogeny class
Conductor	68544	Conductor
∏ cp	432	Product of Tamagawa factors cp
Δ	-4.6639417006928E+22	Discriminant
Eigenvalues	2+ 3- -3 7-  3 -5 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-219860364,1254825734384]	[a1,a2,a3,a4,a6]
Generators	[-17048:219708:1] [8350:-34272:1]	Generators of the group modulo torsion
j	-6150311179917589675873/244053849830826	j-invariant
L	9.2405932966715	L(r)(E,1)/r!
Ω	0.10634397851024	Real period
R	0.20114220438844	Regulator
r	2	Rank of the group of rational points
S	0.99999999999191	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	68544ed3 2142j3 22848o3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 68544cp3

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
+	-	-3	-	3	-5	-	-2	-6	-6	-4	-11	12	1	-12	-9	-12	10	-5	0	-7	-1	-15	-9	-19

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Quadratic twists for elliptic curve 68544cp3

-4	8	-3
68544ed3	2142j3	22848o3

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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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