Cremona's table of elliptic curves

53600 = 2⁵ · 5² · 67

Field	Data	Notes
Atkin-Lehner	2+ 5+ 67+	Signs for the Atkin-Lehner involutions
Class	53600b	Isogeny class
Conductor	53600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	41472	Modular degree for the optimal curve
Δ	-4288000000 = -1 · 212 · 56 · 67	Discriminant
Eigenvalues	2+  2 5+ -4 -2  2 -7 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-333,4037]	[a1,a2,a3,a4,a6]
Generators	[47:300:1]	Generators of the group modulo torsion
j	-64000/67	j-invariant
L	6.6758930544263	L(r)(E,1)/r!
Ω	1.2576658794141	Real period
R	1.3270402663369	Regulator
r	1	Rank of the group of rational points
S	1.0000000000156	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	53600h1 107200cv1 2144b1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 53600b1

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
+	2	+	-4	-2	2	-7	-7	9	3	2	5	10	-4	3	4	-9	14	+	-12	11	-6	4	3	18

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Quadratic twists for elliptic curve 53600b1

-4	8	5
53600h1	107200cv1	2144b1

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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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