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SageMath
E = EllipticCurve("dv1")
E.isogeny_class()
Elliptic curves in class 277200.dv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277200.dv1 | 277200dv3 | \([0, 0, 0, -10766658675, 428440897363250]\) | \(2958414657792917260183849/12401051653985258880\) | \(578583465968336238305280000000\) | \([2]\) | \(462422016\) | \(4.5655\) | |
| 277200.dv2 | 277200dv2 | \([0, 0, 0, -1009218675, -701071276750]\) | \(2436531580079063806249/1405478914998681600\) | \(65574024258178488729600000000\) | \([2, 2]\) | \(231211008\) | \(4.2190\) | |
| 277200.dv3 | 277200dv1 | \([0, 0, 0, -714306675, -7329808300750]\) | \(863913648706111516969/2486234429521920\) | \(115997753543774699520000000\) | \([2]\) | \(115605504\) | \(3.8724\) | \(\Gamma_0(N)\)-optimal |
| 277200.dv4 | 277200dv4 | \([0, 0, 0, 4029629325, -5603870380750]\) | \(155099895405729262880471/90047655797243760000\) | \(-4201263428876204866560000000000\) | \([2]\) | \(462422016\) | \(4.5655\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.dv have rank \(0\).
Complex multiplication
The elliptic curves in class 277200.dv do not have complex multiplication.Modular form 277200.2.a.dv
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
