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	67600g	Isogeny class
Conductor	67600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	55296	Modular degree for the optimal curve
Δ	1056250000 = 24 · 58 · 132	Discriminant
Eigenvalues	2+ -1 5+  3  1 13+ -1 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-10508,-411113]	[a1,a2,a3,a4,a6]
Generators	[-12738:125:216]	Generators of the group modulo torsion
j	3037375744/25	j-invariant
L	5.8120227209366	L(r)(E,1)/r!
Ω	0.47153757861389	Real period
R	3.0814207519309	Regulator
r	1	Rank of the group of rational points
S	1.0000000001225	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	33800f1 13520j1 67600j1	Quadratic twists by: -4 5 13

Hecke Eigenvalues for elliptic curve 67600g1

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	+	3	1	+	-1	-1	-5	3	8	9	5	9	-8	10	3	-5	-3	-1	-14	-8	0	-3	5

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Quadratic twists for elliptic curve 67600g1

-4	5	13
33800f1	13520j1	67600j1

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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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