Cremona's table of elliptic curves

45600 = 2⁵ · 3 · 5² · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 5- 19+	Signs for the Atkin-Lehner involutions
Class	45600bi	Isogeny class
Conductor	45600	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	35840	Modular degree for the optimal curve
Δ	-253344024000 = -1 · 26 · 35 · 53 · 194	Discriminant
Eigenvalues	2- 3+ 5-  2 -2 -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-798,25992]	[a1,a2,a3,a4,a6]
Generators	[-28:160:1]	Generators of the group modulo torsion
j	-7033743296/31668003	j-invariant
L	4.9310727747756	L(r)(E,1)/r!
Ω	0.85630097334476	Real period
R	2.8792871480155	Regulator
r	1	Rank of the group of rational points
S	1.0000000000013	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	45600bx1 91200jd1 45600s1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 45600bi1

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

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Quadratic twists for elliptic curve 45600bi1

-4	8	5
45600bx1	91200jd1	45600s1

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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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