Properties

Label 65520.cz
Number of curves $2$
Conductor $65520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 65520.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
65520.cz1 65520bh1 \([0, 0, 0, -176907, -13482614]\) \(820221748268836/369468094905\) \(275806454974202880\) \([2]\) \(602112\) \(2.0418\) \(\Gamma_0(N)\)-optimal
65520.cz2 65520bh2 \([0, 0, 0, 614013, -100958366]\) \(17147425715207422/12872524043925\) \(-19218575417387673600\) \([2]\) \(1204224\) \(2.3884\)  

Rank

sage: E.rank()
 

The elliptic curves in class 65520.cz have rank \(0\).

Complex multiplication

The elliptic curves in class 65520.cz do not have complex multiplication.

Modular form 65520.2.a.cz

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} + 2 q^{11} + q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.