Properties

Label 705600.bz
Number of curves $2$
Conductor $705600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 705600.bz

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bz1 \([0, 0, 0, -82670700, 289318054480]\) \(266916252066900625/162\) \(37924385587200\) \([]\) \(39813120\) \(2.8282\)
705600.bz2 \([0, 0, 0, -1022700, 395175760]\) \(505318200625/4251528\) \(995287575350476800\) \([]\) \(13271040\) \(2.2789\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.bz have rank \(0\).

Complex multiplication

The elliptic curves in class 705600.bz do not have complex multiplication.

Modular form 705600.2.a.bz

sage: E.q_eigenform(10)
 
\(q - 6 q^{11} + 4 q^{13} + 3 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.