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	68544ca	Isogeny class
Conductor	68544	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	5898240	Modular degree for the optimal curve
Δ	1.0600185040338E+22	Discriminant
Eigenvalues	2+ 3- -2 7-  4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-40460556,-98935513616]	[a1,a2,a3,a4,a6]
Generators	[-40220202:14099729:10648]	Generators of the group modulo torsion
j	38331145780597164097/55468445663232	j-invariant
L	5.7756467928518	L(r)(E,1)/r!
Ω	0.059865875109017	Real period
R	12.059555595485	Regulator
r	1	Rank of the group of rational points
S	0.99999999994032	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68544dq1 2142g1 22848bn1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 68544ca1

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	+	-4	-8	6	0	2	-10	4	0	6	-4	-6	12	8	-6	0	-12	6	2

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Quadratic twists for elliptic curve 68544ca1

-4	8	-3
68544dq1	2142g1	22848bn1

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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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