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Properties

Label 15210.bl
Number of curves $2$
Conductor $15210$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 15210.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.bl1 15210bo1 \([1, -1, 1, -15242, -757519]\) \(-658489/40\) \(-23786707824360\) \([]\) \(44928\) \(1.3216\) \(\Gamma_0(N)\)-optimal
15210.bl2 15210bo2 \([1, -1, 1, 83623, -1232071]\) \(108750551/64000\) \(-38058732518976000\) \([3]\) \(134784\) \(1.8709\)  

Rank

sage: E.rank()
 

The elliptic curves in class 15210.bl have rank \(0\).

Complex multiplication

The elliptic curves in class 15210.bl do not have complex multiplication.

Modular form 15210.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - 3 q^{11} - q^{14} + q^{16} + 6 q^{17} + 5 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.