Properties

Label 705600.bwy
Number of curves $2$
Conductor $705600$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bwy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 705600.bwy

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
705600.bwy1 \([0, 0, 0, -216300, -27538000]\) \(2185454/625\) \(320060160000000000\) \([2]\) \(7077888\) \(2.0655\)
705600.bwy2 \([0, 0, 0, 35700, -2842000]\) \(19652/25\) \(-6401203200000000\) \([2]\) \(3538944\) \(1.7189\)

Rank

sage: E.rank()
 

The elliptic curves in class 705600.bwy have rank \(1\).

Complex multiplication

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

Modular form 705600.2.a.bwy

sage: E.q_eigenform(10)
 
\(q + 4 q^{11} + 2 q^{13} - 2 q^{19} + O(q^{20})\) 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 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.