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Properties

Label 15870.bm
Number of curves $2$
Conductor $15870$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 15870.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15870.bm1 15870bk2 \([1, 0, 0, -415805, 71440377]\) \(53706380371489/16171875000\) \(2394017892421875000\) \([2]\) \(253440\) \(2.2318\)  
15870.bm2 15870bk1 \([1, 0, 0, 70875, 7490625]\) \(265971760991/317400000\) \(-46986591168600000\) \([2]\) \(126720\) \(1.8853\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 15870.bm have rank \(1\).

Complex multiplication

The elliptic curves in class 15870.bm do not have complex multiplication.

Modular form 15870.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 2 q^{11} + q^{12} + q^{15} + q^{16} - 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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 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.