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Properties

Label 162450bs
Number of curves $2$
Conductor $162450$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bs1")
 
E.isogeny_class()
 

Elliptic curves in class 162450bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162450.et2 162450bs1 \([1, -1, 1, -191976980, -51824345353]\) \(212883113611/122880000\) \(451659516827310720000000000\) \([2]\) \(112066560\) \(3.8041\) \(\Gamma_0(N)\)-optimal
162450.et1 162450bs2 \([1, -1, 1, -2167368980, -38737901273353]\) \(306331959547531/900000000\) \(3308053101762529687500000000\) \([2]\) \(224133120\) \(4.1507\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162450bs have rank \(1\).

Complex multiplication

The elliptic curves in class 162450bs do not have complex multiplication.

Modular form 162450.2.a.bs

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