Properties

Label 262080.e
Number of curves $2$
Conductor $262080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 262080.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
262080.e1 262080e1 \([0, 0, 0, -19525068, -30560756112]\) \(4307585705106105969/381542350192640\) \(72913878591847677296640\) \([2]\) \(32440320\) \(3.1271\) \(\Gamma_0(N)\)-optimal
262080.e2 262080e2 \([0, 0, 0, 21762612, -142582489488]\) \(5964709808210123151/49408483478681600\) \(-9442108232422886316441600\) \([2]\) \(64880640\) \(3.4737\)  

Rank

sage: E.rank()
 

The elliptic curves in class 262080.e have rank \(0\).

Complex multiplication

The elliptic curves in class 262080.e do not have complex multiplication.

Modular form 262080.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 6 q^{11} - q^{13} + 8 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.