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Properties

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

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Show commands: SageMath
E = EllipticCurve("cl1")
 
E.isogeny_class()
 

Elliptic curves in class 95550cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.x2 95550cl1 \([1, 1, 0, -1495, 47125]\) \(-25153757/52416\) \(-770836248000\) \([2]\) \(129024\) \(0.97000\) \(\Gamma_0(N)\)-optimal
95550.x1 95550cl2 \([1, 1, 0, -30895, 2075725]\) \(221774710877/198744\) \(2922754107000\) \([2]\) \(258048\) \(1.3166\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 95550.2.a.cl

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