Cremona's table of elliptic curves

122400 = 2⁵ · 3² · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 17-	Signs for the Atkin-Lehner involutions
Class	122400ei	Isogeny class
Conductor	122400	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	103680	Modular degree for the optimal curve
Δ	-31726080000 = -1 · 212 · 36 · 54 · 17	Discriminant
Eigenvalues	2- 3- 5- -3  0 -5 17- -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-300,-8800]	[a1,a2,a3,a4,a6]
Generators	[29:83:1]	Generators of the group modulo torsion
j	-1600/17	j-invariant
L	3.7638458881151	L(r)(E,1)/r!
Ω	0.49742296377891	Real period
R	3.7833454984819	Regulator
r	1	Rank of the group of rational points
S	1.0000000070157	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	122400bx1 13600h1 122400x1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 122400ei1

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
-	-	-	-3	0	-5	-	-8	-8	-2	-3	-2	12	-10	2	9	14	6	4	-7	2	-11	0	14	0

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Quadratic twists for elliptic curve 122400ei1

-4	-3	5
122400bx1	13600h1	122400x1

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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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