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	51744by	Isogeny class
Conductor	51744	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	49152	Modular degree for the optimal curve
Δ	73796982336 = 26 · 34 · 76 · 112	Discriminant
Eigenvalues	2- 3+  2 7- 11+  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1682,-22560]	[a1,a2,a3,a4,a6]
Generators	[322:5720:1]	Generators of the group modulo torsion
j	69934528/9801	j-invariant
L	6.4667458557538	L(r)(E,1)/r!
Ω	0.75240013309105	Real period
R	4.2974114246941	Regulator
r	1	Rank of the group of rational points
S	0.99999999999694	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	51744bq1 103488ef2 1056i1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 51744by1

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	-	+	6	-2	4	-4	2	4	-2	-10	-4	4	6	12	6	-4	-4	-10	-16	-4	-10	-2

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Quadratic twists for elliptic curve 51744by1

-4	8	-7
51744bq1	103488ef2	1056i1

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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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