Properties

Label 253575bf
Number of curves $2$
Conductor $253575$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 253575bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
253575.bf1 253575bf1 \([1, -1, 1, -1793630, -923806628]\) \(476196576129/197225\) \(264300362722265625\) \([2]\) \(5308416\) \(2.3050\) \(\Gamma_0(N)\)-optimal
253575.bf2 253575bf2 \([1, -1, 1, -1518005, -1217622878]\) \(-288673724529/311181605\) \(-417013112303190703125\) \([2]\) \(10616832\) \(2.6515\)  

Rank

sage: E.rank()
 

The elliptic curves in class 253575bf have rank \(0\).

Complex multiplication

The elliptic curves in class 253575bf do not have complex multiplication.

Modular form 253575.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 3 q^{8} - 2 q^{11} + 4 q^{13} - q^{16} + 6 q^{17} + 8 q^{19} + O(q^{20})\) 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.