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	51744k	Isogeny class
Conductor	51744	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	552960	Modular degree for the optimal curve
Δ	6509558014876224 = 26 · 310 · 76 · 114	Discriminant
Eigenvalues	2+ 3+ -2 7- 11+  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-960514,-361988696]	[a1,a2,a3,a4,a6]
j	13015685560572352/864536409	j-invariant
L	0.30500384800903	L(r)(E,1)/r!
Ω	0.15250192406472	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	51744cq1 103488dx2 1056d1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 51744k1

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	-4	-2	6	-4	8	-6	-12	10	4	0	-10	12	-12	-10	-18

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Quadratic twists for elliptic curve 51744k1

-4	8	-7
51744cq1	103488dx2	1056d1

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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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