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Properties

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

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 95550cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.a2 95550cn1 \([1, 1, 0, -7365950, 155232016500]\) \(-961749189765625/225967964931072\) \(-10384728557099878800000000\) \([]\) \(25920000\) \(3.4795\) \(\Gamma_0(N)\)-optimal
95550.a1 95550cn2 \([1, 1, 0, -2425975325, 45991846192125]\) \(-34358530063612633515625/1163438994751488\) \(-53467747770905395200000000\) \([]\) \(77760000\) \(4.0288\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 95550.2.a.cn

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.