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	68400ep	Isogeny class
Conductor	68400	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	491520	Modular degree for the optimal curve
Δ	-20464021440000000 = -1 · 212 · 311 · 57 · 192	Discriminant
Eigenvalues	2- 3- 5+ -2 -6  0 -6 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,68325,-341750]	[a1,a2,a3,a4,a6]
Generators	[119:-3078:1]	Generators of the group modulo torsion
j	756058031/438615	j-invariant
L	4.2160768327857	L(r)(E,1)/r!
Ω	0.22781506429512	Real period
R	1.1566610087075	Regulator
r	1	Rank of the group of rational points
S	0.99999999993454	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4275l1 22800cz1 13680bl1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 68400ep1

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	-6	0	-6	+	8	-4	0	-4	0	-2	8	2	12	2	-8	16	-14	-8	0	0	12

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Quadratic twists for elliptic curve 68400ep1

-4	-3	5
4275l1	22800cz1	13680bl1

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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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