Cremona's table of elliptic curves

123200 = 2⁶ · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	123200fs	Isogeny class
Conductor	123200	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	2654208	Modular degree for the optimal curve
Δ	-1.74076198912E+19	Discriminant
Eigenvalues	2-  2 5+ 7- 11+ -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-89633,-200972863]	[a1,a2,a3,a4,a6]
Generators	[53008:12203961:1]	Generators of the group modulo torsion
j	-19443408769/4249907200	j-invariant
L	9.8328124006055	L(r)(E,1)/r!
Ω	0.097676032857891	Real period
R	8.3889671686106	Regulator
r	1	Rank of the group of rational points
S	1.0000000007064	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	123200bf1 30800ca1 24640bt1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 123200fs1

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	0	-4	0	6	10	2	-12	4	6	-6	-6	4	4	-12	4	-8	-12	18	10

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Quadratic twists for elliptic curve 123200fs1

-4	8	5
123200bf1	30800ca1	24640bt1

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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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