Cremona's table of elliptic curves

61200 = 2⁴ · 3² · 5² · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 17+	Signs for the Atkin-Lehner involutions
Class	61200ey	Isogeny class
Conductor	61200	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	122880	Modular degree for the optimal curve
Δ	28553472000000 = 214 · 38 · 56 · 17	Discriminant
Eigenvalues	2- 3- 5+ -2  0  6 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-9075,211250]	[a1,a2,a3,a4,a6]
Generators	[-25:650:1]	Generators of the group modulo torsion
j	1771561/612	j-invariant
L	5.9522790490902	L(r)(E,1)/r!
Ω	0.61036459505709	Real period
R	2.4380014409902	Regulator
r	1	Rank of the group of rational points
S	0.99999999999596	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7650o1 20400ch1 2448t1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 61200ey1

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

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Quadratic twists for elliptic curve 61200ey1

-4	-3	5
7650o1	20400ch1	2448t1

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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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