Properties

Label 35280.v
Number of curves $2$
Conductor $35280$
CM no
Rank $0$
Graph

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

Elliptic curves in class 35280.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35280.v1 35280eg1 \([0, 0, 0, -18963, -1005102]\) \(-5154200289/20\) \(-2926264320\) \([]\) \(40320\) \(1.0296\) \(\Gamma_0(N)\)-optimal
35280.v2 35280eg2 \([0, 0, 0, 132237, 9536562]\) \(1747829720511/1280000000\) \(-187280916480000000\) \([]\) \(282240\) \(2.0026\)  

Rank

sage: E.rank()
 

The elliptic curves in class 35280.v have rank \(0\).

Complex multiplication

The elliptic curves in class 35280.v do not have complex multiplication.

Modular form 35280.2.a.v

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2 q^{11} - 4 q^{17} - 6 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.