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Properties

Label 63426ba
Number of curves $2$
Conductor $63426$
CM no
Rank $0$
Graph

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

Elliptic curves in class 63426ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
63426.t2 63426ba1 \([1, 1, 1, -1866282, 1390884087]\) \(-877078753/513216\) \(-420646350931138766016\) \([]\) \(4017600\) \(2.6600\) \(\Gamma_0(N)\)-optimal
63426.t1 63426ba2 \([1, 1, 1, -168100062, 838810174215]\) \(-640929697062433/47916\) \(-39273308998972060716\) \([]\) \(12052800\) \(3.2093\)  

Rank

sage: E.rank()
 

The elliptic curves in class 63426ba have rank \(0\).

Complex multiplication

The elliptic curves in class 63426ba do not have complex multiplication.

Modular form 63426.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 3 q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} - 3 q^{10} + q^{11} - q^{12} - 2 q^{13} + 2 q^{14} + 3 q^{15} + q^{16} - 6 q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.