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Properties

Label 48510bm
Number of curves $2$
Conductor $48510$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 48510bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48510.bl2 48510bm1 \([1, -1, 0, 4401, -454707]\) \(109902239/1100000\) \(-94342733100000\) \([]\) \(198000\) \(1.3626\) \(\Gamma_0(N)\)-optimal
48510.bl1 48510bm2 \([1, -1, 0, -2619549, -1631224197]\) \(-23178622194826561/1610510\) \(-138127195531710\) \([]\) \(990000\) \(2.1673\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48510bm have rank \(0\).

Complex multiplication

The elliptic curves in class 48510bm do not have complex multiplication.

Modular form 48510.2.a.bm

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - q^{11} + 6 q^{13} + q^{16} - 7 q^{17} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.