Cremona's table of elliptic curves

67600 = 2⁴ · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	67600bt	Isogeny class
Conductor	67600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	48384	Modular degree for the optimal curve
Δ	401590508800 = 28 · 52 · 137	Discriminant
Eigenvalues	2- -1 5+ -2 -2 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2253,28417]	[a1,a2,a3,a4,a6]
Generators	[13:34:1] [61:-338:1]	Generators of the group modulo torsion
j	40960/13	j-invariant
L	7.8972921654167	L(r)(E,1)/r!
Ω	0.87591143625839	Real period
R	1.1270106540633	Regulator
r	2	Rank of the group of rational points
S	0.999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16900c1 67600cx1 5200x1	Quadratic twists by: -4 5 13

Hecke Eigenvalues for elliptic curve 67600bt1

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
-	-1	+	-2	-2	+	-2	0	-3	-7	-6	4	8	-1	0	1	4	-1	-6	-8	-14	-5	0	14	-4

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Quadratic twists for elliptic curve 67600bt1

-4	5	13
16900c1	67600cx1	5200x1

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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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