Properties

Label 234416z
Number of curves $2$
Conductor $234416$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 234416z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
234416.z2 234416z1 \([0, 0, 0, -10780, -429093]\) \(73598976000/336973\) \(634312583632\) \([2]\) \(276480\) \(1.1155\) \(\Gamma_0(N)\)-optimal
234416.z1 234416z2 \([0, 0, 0, -16415, 67914]\) \(16241202000/9332687\) \(281083210972928\) \([2]\) \(552960\) \(1.4621\)  

Rank

sage: E.rank()
 

The elliptic curves in class 234416z have rank \(1\).

Complex multiplication

The elliptic curves in class 234416z do not have complex multiplication.

Modular form 234416.2.a.z

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