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	36800o	Isogeny class
Conductor	36800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	314880	Modular degree for the optimal curve
Δ	-32181715000000 = -1 · 26 · 57 · 235	Discriminant
Eigenvalues	2+ -2 5+ -3 -6  4 -7 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-182383,-30041637]	[a1,a2,a3,a4,a6]
Generators	[1082:32257:1]	Generators of the group modulo torsion
j	-670933008285184/32181715	j-invariant
L	1.6615299557472	L(r)(E,1)/r!
Ω	0.11551064847146	Real period
R	7.1921072980442	Regulator
r	1	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	36800ba1 18400o1 7360n1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 36800o1

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	+	-3	-6	4	-7	-8	+	-3	-11	7	5	-12	12	7	-5	-2	-1	3	0	12	-5	-6	-10

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Quadratic twists for elliptic curve 36800o1

-4	8	5
36800ba1	18400o1	7360n1

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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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