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	123200el	Isogeny class
Conductor	123200	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	786432	Modular degree for the optimal curve
Δ	-10494668800000000 = -1 · 218 · 58 · 7 · 114	Discriminant
Eigenvalues	2-  0 5+ 7+ 11- -6 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-58700,-7366000]	[a1,a2,a3,a4,a6]
Generators	[565:11825:1]	Generators of the group modulo torsion
j	-5461074081/2562175	j-invariant
L	3.7952588555506	L(r)(E,1)/r!
Ω	0.14998297675415	Real period
R	3.1630746852923	Regulator
r	1	Rank of the group of rational points
S	0.99999999989035	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	123200bl1 30800z1 24640bo1	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 123200el1

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

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Quadratic twists for elliptic curve 123200el1

-4	8	5
123200bl1	30800z1	24640bo1

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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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