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	61200gw	Isogeny class
Conductor	61200	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	819200	Modular degree for the optimal curve
Δ	-409563864000000000 = -1 · 212 · 311 · 59 · 172	Discriminant
Eigenvalues	2- 3- 5-  4  6  4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-10875,-30793750]	[a1,a2,a3,a4,a6]
j	-24389/70227	j-invariant
L	4.3399849547836	L(r)(E,1)/r!
Ω	0.13562452969116	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3825m1 20400ct1 61200hl1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 61200gw1

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

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Quadratic twists for elliptic curve 61200gw1

-4	-3	5
3825m1	20400ct1	61200hl1

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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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