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Properties

Label 95550.iz
Number of curves $4$
Conductor $95550$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("iz1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 95550.iz have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(7\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 + 4 T + 11 T^{2}\) 1.11.e
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 + 8 T + 19 T^{2}\) 1.19.i
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 95550.iz do not have complex multiplication.

Modular form 95550.2.a.iz

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 4 q^{11} + q^{12} - q^{13} + q^{16} - 2 q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 95550.iz

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.iz1 95550jl4 \([1, 0, 0, -405413729813, 61761071350771617]\) \(4008766897254067912673785886329/1423480510711669921875000000\) \(2616735290698707103729248046875000000\) \([2]\) \(1981808640\) \(5.6890\)  
95550.iz2 95550jl2 \([1, 0, 0, -171369737813, -26602003784836383]\) \(302773487204995438715379645049/8911747415025000000000000\) \(16382158931723066015625000000000000\) \([2, 2]\) \(990904320\) \(5.3424\)  
95550.iz3 95550jl1 \([1, 0, 0, -170140425813, -27012157587076383]\) \(296304326013275547793071733369/268420373544960000000\) \(493427945737359360000000000000\) \([2]\) \(495452160\) \(4.9958\) \(\Gamma_0(N)\)-optimal
95550.iz4 95550jl3 \([1, 0, 0, 43005262187, -88715230659836383]\) \(4784981304203817469820354951/1852343836482910078035000000\) \(-3405100000287154496417808046875000000\) \([2]\) \(1981808640\) \(5.6890\)