Properties

Label 34650cm
Number of curves $2$
Conductor $34650$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 34650cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34650.cu1 34650cm1 \([1, -1, 1, -4708505, -3930858503]\) \(37537160298467283/5519360000\) \(1697461920000000000\) \([2]\) \(1032192\) \(2.5122\) \(\Gamma_0(N)\)-optimal
34650.cu2 34650cm2 \([1, -1, 1, -4276505, -4681674503]\) \(-28124139978713043/14526050000000\) \(-4467441283593750000000\) \([2]\) \(2064384\) \(2.8588\)  

Rank

sage: E.rank()
 

The elliptic curves in class 34650cm have rank \(0\).

Complex multiplication

The elliptic curves in class 34650cm do not have complex multiplication.

Modular form 34650.2.a.cm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{7} + q^{8} - q^{11} + 4 q^{13} - q^{14} + q^{16} - 2 q^{17} - 6 q^{19} + O(q^{20})\) 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 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.