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Properties

Label 244398bs
Number of curves $2$
Conductor $244398$
CM no
Rank $0$
Graph

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

Elliptic curves in class 244398bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
244398.bs2 244398bs1 \([1, 0, 0, 2041929, -377667927]\) \(6360314548472639/4097346156288\) \(-606554280786827020032\) \([2]\) \(14598144\) \(2.6768\) \(\Gamma_0(N)\)-optimal
244398.bs1 244398bs2 \([1, 0, 0, -8665031, -3107942727]\) \(486034459476995521/253095136942032\) \(37467163598790448586448\) \([2]\) \(29196288\) \(3.0234\)  

Rank

sage: E.rank()
 

The elliptic curves in class 244398bs have rank \(0\).

Complex multiplication

The elliptic curves in class 244398bs do not have complex multiplication.

Modular form 244398.2.a.bs

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + 4 q^{10} - q^{11} + q^{12} - q^{14} + 4 q^{15} + q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) 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.