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Properties

Label 95550la
Number of curves $2$
Conductor $95550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("la1")
 
E.isogeny_class()
 

Elliptic curves in class 95550la

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.iu2 95550la1 \([1, 0, 0, -19013, 875517]\) \(3307949/468\) \(107538539062500\) \([2]\) \(491520\) \(1.4183\) \(\Gamma_0(N)\)-optimal
95550.iu1 95550la2 \([1, 0, 0, -80263, -7883233]\) \(248858189/27378\) \(6291004535156250\) \([2]\) \(983040\) \(1.7649\)  

Rank

sage: E.rank()
 

The elliptic curves in class 95550la have rank \(1\).

Complex multiplication

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

Modular form 95550.2.a.la

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

Isogeny matrix

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.