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Properties

Label 155610bp
Number of curves $2$
Conductor $155610$
CM no
Rank $0$
Graph

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

Elliptic curves in class 155610bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
155610.db1 155610bp1 \([1, -1, 1, -433508, -109751673]\) \(12359092816971484921/116188800000\) \(84701635200000\) \([2]\) \(2048000\) \(1.8354\) \(\Gamma_0(N)\)-optimal
155610.db2 155610bp2 \([1, -1, 1, -423428, -115106169]\) \(-11516856136356002041/1201114687500000\) \(-875612607187500000\) \([2]\) \(4096000\) \(2.1819\)  

Rank

sage: E.rank()
 

The elliptic curves in class 155610bp have rank \(0\).

Complex multiplication

The elliptic curves in class 155610bp do not have complex multiplication.

Modular form 155610.2.a.bp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} - 4 q^{11} - q^{13} - q^{14} + q^{16} + 6 q^{17} + q^{19} + O(q^{20})\) 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.