Cremona's table of elliptic curves

36800 = 2⁶ · 5² · 23

Field	Data	Notes
Atkin-Lehner	2+ 5+ 23+	Signs for the Atkin-Lehner involutions
Class	36800j	Isogeny class
Conductor	36800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96768	Modular degree for the optimal curve
Δ	-950546875000000 = -1 · 26 · 513 · 233	Discriminant
Eigenvalues	2+  2 5+  1  2  0  1 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,617,1483137]	[a1,a2,a3,a4,a6]
Generators	[385920:21441027:125]	Generators of the group modulo torsion
j	25934336/950546875	j-invariant
L	8.8405780051498	L(r)(E,1)/r!
Ω	0.39198474362035	Real period
R	11.276686336692	Regulator
r	1	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36800bd1 18400d1 7360o1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 36800j1

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	+	1	2	0	1	-4	+	5	-7	-1	5	-4	4	-1	-9	10	3	-9	-4	-4	-17	6	14

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Quadratic twists for elliptic curve 36800j1

-4	8	5
36800bd1	18400d1	7360o1

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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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