Cremona's table of elliptic curves

45920 = 2⁵ · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 41-	Signs for the Atkin-Lehner involutions
Class	45920b	Isogeny class
Conductor	45920	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	39936	Modular degree for the optimal curve
Δ	658952000 = 26 · 53 · 72 · 412	Discriminant
Eigenvalues	2+  0 5+ 7+ -4 -4 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8153,283348]	[a1,a2,a3,a4,a6]
Generators	[-12:616:1] [51:14:1]	Generators of the group modulo torsion
j	936474735013056/10296125	j-invariant
L	8.0032086220872	L(r)(E,1)/r!
Ω	1.465395700431	Real period
R	2.7307329411892	Regulator
r	2	Rank of the group of rational points
S	0.99999999999992	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45920e1 91840o2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 45920b1

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
+	0	+	+	-4	-4	-4	4	2	6	-4	-2	-	10	-8	-12	-4	-2	-4	-16	-14	8	-6	10	-16

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Quadratic twists for elliptic curve 45920b1

-4	8
45920e1	91840o2

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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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