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Properties

Label 53067.f
Number of curves $2$
Conductor $53067$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 53067.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53067.f1 53067w2 \([0, 1, 1, -329352, -72919276]\) \(-1713910976512/1594323\) \(-3675310176544587\) \([]\) \(560196\) \(1.9096\)  
53067.f2 53067w1 \([0, 1, 1, -842, 9944]\) \(-28672/3\) \(-6915744507\) \([]\) \(43092\) \(0.62713\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 53067.f have rank \(0\).

Complex multiplication

The elliptic curves in class 53067.f do not have complex multiplication.

Modular form 53067.2.a.f

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + q^{9} - 4 q^{10} - 2 q^{11} + 2 q^{12} + q^{13} + 2 q^{15} - 4 q^{16} - 2 q^{18} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.