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	67600cl	Isogeny class
Conductor	67600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1128960	Modular degree for the optimal curve
Δ	-514035851264000000 = -1 · 219 · 56 · 137	Discriminant
Eigenvalues	2- -3 5+ -1 -2 13+  3  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-181675,-45587750]	[a1,a2,a3,a4,a6]
j	-2146689/1664	j-invariant
L	0.44753151535263	L(r)(E,1)/r!
Ω	0.11188287758242	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8450t1 2704j1 5200bc1	Quadratic twists by: -4 5 13

Hecke Eigenvalues for elliptic curve 67600cl1

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
-	-3	+	-1	-2	+	3	6	-4	2	4	3	0	-5	-13	-12	-10	-8	2	-5	-10	4	0	-6	14

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Quadratic twists for elliptic curve 67600cl1

-4	5	13
8450t1	2704j1	5200bc1

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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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