Properties

Label 64400bl
Number of curves $2$
Conductor $64400$
CM no
Rank $1$
Graph

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

Elliptic curves in class 64400bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.e2 64400bl1 \([0, 1, 0, -5608, -43212]\) \(304821217/164864\) \(10551296000000\) \([2]\) \(122880\) \(1.1899\) \(\Gamma_0(N)\)-optimal
64400.e1 64400bl2 \([0, 1, 0, -69608, -7083212]\) \(582810602977/829472\) \(53086208000000\) \([2]\) \(245760\) \(1.5365\)  

Rank

sage: E.rank()
 

The elliptic curves in class 64400bl have rank \(1\).

Complex multiplication

The elliptic curves in class 64400bl do not have complex multiplication.

Modular form 64400.2.a.bl

sage: E.q_eigenform(10)
 
\(q - 2q^{3} - q^{7} + q^{9} + 2q^{11} + 4q^{13} + 6q^{17} + O(q^{20})\)  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.