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	8	Product of Tamagawa factors cp
Δ	-7937275433472 = -1 · 29 · 32 · 76 · 114	Discriminant
Eigenvalues	2- 3+  2 7- 11+  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,2728,-124872]	[a1,a2,a3,a4,a6]
Generators	[429620:3333421:8000]	Generators of the group modulo torsion
j	37259704/131769	j-invariant
L	6.4667458557538	L(r)(E,1)/r!
Ω	0.37620006654553	Real period
R	8.5948228493881	Regulator
r	1	Rank of the group of rational points
S	0.99999999999694	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	51744bq2 103488ef3 1056i4	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 51744by2

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 51744by2

-4	8	-7
51744bq2	103488ef3	1056i4

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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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