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Properties

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

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Show commands: SageMath
E = EllipticCurve("fw1")
 
E.isogeny_class()
 

Elliptic curves in class 95550fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.dd2 95550fw1 \([1, 0, 1, -395701, 1514048]\) \(29819839301/17252352\) \(3964300704000000000\) \([2]\) \(2580480\) \(2.2581\) \(\Gamma_0(N)\)-optimal
95550.dd1 95550fw2 \([1, 0, 1, -4315701, -3440245952]\) \(38686490446661/141927552\) \(32612567510250000000\) \([2]\) \(5160960\) \(2.6047\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 95550.2.a.fw

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