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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 162240v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162240.ih4 | 162240v1 | \([0, 1, 0, -1551645, 626681043]\) | \(83587439220736/13990184325\) | \(69148618354246579200\) | \([2]\) | \(4128768\) | \(2.5280\) | \(\Gamma_0(N)\)-optimal |
| 162240.ih2 | 162240v2 | \([0, 1, 0, -23727825, 44477859375]\) | \(18681746265374416/693005625\) | \(54804574827325440000\) | \([2, 2]\) | \(8257536\) | \(2.8746\) | |
| 162240.ih1 | 162240v3 | \([0, 1, 0, -379641825, 2847015878175]\) | \(19129597231400697604/26325\) | \(8327380790476800\) | \([2]\) | \(16515072\) | \(3.2211\) | |
| 162240.ih3 | 162240v4 | \([0, 1, 0, -22632705, 48770072703]\) | \(-4053153720264484/903687890625\) | \(-285863368698086400000000\) | \([2]\) | \(16515072\) | \(3.2211\) |
Rank
sage: E.rank()
The elliptic curves in class 162240v have rank \(0\).
Complex multiplication
The elliptic curves in class 162240v do not have complex multiplication.Modular form 162240.2.a.v
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 Cremona 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 Cremona labels.
