Cremona's table of elliptic curves

68400 = 2⁴ · 3² · 5² · 19

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 19-	Signs for the Atkin-Lehner involutions
Class	68400k	Isogeny class
Conductor	68400	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	614400	Modular degree for the optimal curve
Δ	-175933350000000000 = -1 · 210 · 33 · 511 · 194	Discriminant
Eigenvalues	2+ 3+ 5+ -2  2  0 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5925,-20179750]	[a1,a2,a3,a4,a6]
Generators	[2690:-35625:8] [379:6042:1]	Generators of the group modulo torsion
j	53248212/407253125	j-invariant
L	10.263988674615	L(r)(E,1)/r!
Ω	0.14839546504387	Real period
R	2.1614518070876	Regulator
r	2	Rank of the group of rational points
S	0.99999999999703	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	34200e1 68400l1 13680b1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 68400k1

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	2	0	-6	-	-8	-6	-4	-4	-4	-12	0	-14	-10	10	4	4	2	-4	-12	0	-6

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Quadratic twists for elliptic curve 68400k1

-4	-3	5
34200e1	68400l1	13680b1

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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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