Properties

Label 57960.bp
Number of curves $2$
Conductor $57960$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 57960.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57960.bp1 57960f1 \([0, 0, 0, -87, -86]\) \(10536048/5635\) \(38949120\) \([2]\) \(15360\) \(0.14774\) \(\Gamma_0(N)\)-optimal
57960.bp2 57960f2 \([0, 0, 0, 333, -674]\) \(147704148/92575\) \(-2559513600\) \([2]\) \(30720\) \(0.49432\)  

Rank

sage: E.rank()
 

The elliptic curves in class 57960.bp have rank \(0\).

Complex multiplication

The elliptic curves in class 57960.bp do not have complex multiplication.

Modular form 57960.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{5} + q^{7} - 4q^{11} + 4q^{13} + 2q^{17} + 4q^{19} + O(q^{20})\)  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.