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Properties

Label 361998.ba
Number of curves $2$
Conductor $361998$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 361998.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361998.ba1 361998ba2 \([1, -1, 0, -21267, 1199043]\) \(664196078125/14994\) \(24014585322\) \([2]\) \(614400\) \(1.1060\)  
361998.ba2 361998ba1 \([1, -1, 0, -1377, 17577]\) \(180362125/24276\) \(38880757188\) \([2]\) \(307200\) \(0.75939\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 361998.ba have rank \(1\).

Complex multiplication

The elliptic curves in class 361998.ba do not have complex multiplication.

Modular form 361998.2.a.ba

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.