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Properties

Label 348726co
Number of curves $2$
Conductor $348726$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("co1")
 
E.isogeny_class()
 

Elliptic curves in class 348726co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.co2 348726co1 \([1, 0, 0, 120386, -37145020]\) \(4101378352343/15049939968\) \(-708037684791671808\) \([2]\) \(6289920\) \(2.1080\) \(\Gamma_0(N)\)-optimal
348726.co1 348726co2 \([1, 0, 0, -1208094, -446582556]\) \(4144806984356137/568114785504\) \(26727460593161709024\) \([2]\) \(12579840\) \(2.4546\)  

Rank

sage: E.rank()
 

The elliptic curves in class 348726co have rank \(0\).

Complex multiplication

The elliptic curves in class 348726co do not have complex multiplication.

Modular form 348726.2.a.co

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - 2 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - 2 q^{10} + q^{12} - 4 q^{13} - q^{14} - 2 q^{15} + q^{16} + q^{18} + O(q^{20})\) 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.