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	68400bd	Isogeny class
Conductor	68400	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	179712	Modular degree for the optimal curve
Δ	1350056970000 = 24 · 39 · 54 · 193	Discriminant
Eigenvalues	2+ 3+ 5- -5 -4 -2 -4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-33075,-2314575]	[a1,a2,a3,a4,a6]
Generators	[-104:19:1]	Generators of the group modulo torsion
j	20329747200/6859	j-invariant
L	3.077551665803	L(r)(E,1)/r!
Ω	0.35402455443737	Real period
R	1.4488409664347	Regulator
r	1	Rank of the group of rational points
S	1.0000000000803	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	34200o1 68400bc1 68400r1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 68400bd1

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
+	+	-	-5	-4	-2	-4	-	-4	-5	2	0	9	-4	-4	3	1	-5	-2	3	-9	-6	4	9	-8

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Quadratic twists for elliptic curve 68400bd1

-4	-3	5
34200o1	68400bc1	68400r1

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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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