Cremona's table of elliptic curves

51392 = 2⁶ · 11 · 73

Field	Data	Notes
Atkin-Lehner	2+ 11+ 73+	Signs for the Atkin-Lehner involutions
Class	51392b	Isogeny class
Conductor	51392	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	189696	Modular degree for the optimal curve
Δ	-2419075761344 = -1 · 26 · 113 · 734	Discriminant
Eigenvalues	2+ -1 -1 -4 11+  6  8 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-54911,-4934951]	[a1,a2,a3,a4,a6]
Generators	[174074288:2180781341:493039]	Generators of the group modulo torsion
j	-286107805145529856/37798058771	j-invariant
L	3.3179772701997	L(r)(E,1)/r!
Ω	0.1559375187394	Real period
R	10.638803595985	Regulator
r	1	Rank of the group of rational points
S	0.99999999999163	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	51392e1 25696b1	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 51392b1

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
+	-1	-1	-4	+	6	8	-2	-3	0	-11	-3	10	-2	12	-10	9	4	5	-13	+	-14	-14	-13	5

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Quadratic twists for elliptic curve 51392b1

-4	8
51392e1	25696b1

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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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