Cremona's table of elliptic curves

51744 = 2⁵ · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11-	Signs for the Atkin-Lehner involutions
Class	51744cm	Isogeny class
Conductor	51744	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	401783570496 = 26 · 32 · 78 · 112	Discriminant
Eigenvalues	2- 3-  2 7- 11-  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7562,-253800]	[a1,a2,a3,a4,a6]
Generators	[-4425300:-3344985:85184]	Generators of the group modulo torsion
j	6352182208/53361	j-invariant
L	9.3297326259144	L(r)(E,1)/r!
Ω	0.51221898276887	Real period
R	9.1071718735244	Regulator
r	1	Rank of the group of rational points
S	0.99999999999985	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	51744g1 103488bc2 7392j1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 51744cm1

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	-	-	2	-2	4	0	6	-8	-10	-2	0	-12	-6	-4	-14	4	0	10	-8	16	6	-2

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Quadratic twists for elliptic curve 51744cm1

-4	8	-7
51744g1	103488bc2	7392j1

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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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