Properties

Label 244398.bl
Number of curves $2$
Conductor $244398$
CM no
Rank $1$
Graph

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

Elliptic curves in class 244398.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
244398.bl1 244398bl2 \([1, 0, 0, -16126949526408, 24927368290379869248]\) \(-3133382230165522315000208250857964625/153574604080128\) \(-22734553042824775713792\) \([]\) \(4742115840\) \(5.6822\)  
244398.bl2 244398bl1 \([1, 0, 0, -199096393608, 34194536777001024]\) \(-5895856113332931416918127084625/215771481613620039647232\) \(-31941923101519397077393235509248\) \([]\) \(1580705280\) \(5.1329\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 244398.bl have rank \(1\).

Complex multiplication

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

Modular form 244398.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} + q^{11} + q^{12} - q^{13} - q^{14} + q^{16} + 3 q^{17} + q^{18} - 5 q^{19} + O(q^{20})\) 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.