Properties

Label 350064q
Number of curves $2$
Conductor $350064$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 350064q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.q2 350064q1 \([0, 0, 0, -4566, -132325]\) \(-902576293888/126190779\) \(-1471889246256\) \([2]\) \(475136\) \(1.0662\) \(\Gamma_0(N)\)-optimal
350064.q1 350064q2 \([0, 0, 0, -75351, -7961146]\) \(253526452425808/4091373\) \(763548394752\) \([2]\) \(950272\) \(1.4128\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350064q have rank \(0\).

Complex multiplication

The elliptic curves in class 350064q do not have complex multiplication.

Modular form 350064.2.a.q

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + 2 q^{7} - q^{11} + q^{13} + q^{17} + 4 q^{19} + O(q^{20})\) 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.