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	67600de	Isogeny class
Conductor	67600	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2419200	Modular degree for the optimal curve
Δ	-2610338307200000000 = -1 · 213 · 58 · 138	Discriminant
Eigenvalues	2- -3 5-  0 -3 13+ -7  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1499875,-711278750]	[a1,a2,a3,a4,a6]
Generators	[1625:33800:1]	Generators of the group modulo torsion
j	-48317985/338	j-invariant
L	2.4291538713668	L(r)(E,1)/r!
Ω	0.068182718418705	Real period
R	1.4844633215945	Regulator
r	1	Rank of the group of rational points
S	0.99999999981342	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8450l1 67600ci1 5200bk1	Quadratic twists by: -4 5 13

Hecke Eigenvalues for elliptic curve 67600de1

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	-	0	-3	+	-7	1	4	4	-10	-12	5	-12	-4	6	-4	4	-5	0	11	-4	15	11	2

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Quadratic twists for elliptic curve 67600de1

-4	5	13
8450l1	67600ci1	5200bk1

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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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