Properties

Label 134640v
Number of curves $2$
Conductor $134640$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("v1")
 
E.isogeny_class()
 

Elliptic curves in class 134640v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
134640.ed1 134640v1 \([0, 0, 0, -1224507, 521536106]\) \(68001744211490809/1022422500\) \(3052937226240000\) \([2]\) \(1548288\) \(2.1078\) \(\Gamma_0(N)\)-optimal
134640.ed2 134640v2 \([0, 0, 0, -1188507, 553640906]\) \(-62178675647294809/8362782148050\) \(-24971133689562931200\) \([2]\) \(3096576\) \(2.4544\)  

Rank

sage: E.rank()
 

The elliptic curves in class 134640v have rank \(0\).

Complex multiplication

The elliptic curves in class 134640v do not have complex multiplication.

Modular form 134640.2.a.v

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{11} + 4 q^{13} - q^{17} + 8 q^{19} + O(q^{20})\) 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.