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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 177744da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 177744.l3 | 177744da1 | \([0, -1, 0, -3879, -91086]\) | \(2725888/21\) | \(49740058704\) | \([2]\) | \(197120\) | \(0.88156\) | \(\Gamma_0(N)\)-optimal |
| 177744.l2 | 177744da2 | \([0, -1, 0, -6524, 51744]\) | \(810448/441\) | \(16712659724544\) | \([2, 2]\) | \(394240\) | \(1.2281\) | |
| 177744.l1 | 177744da3 | \([0, -1, 0, -80584, 8820448]\) | \(381775972/567\) | \(85950821440512\) | \([2]\) | \(788480\) | \(1.5747\) | |
| 177744.l4 | 177744da4 | \([0, -1, 0, 25216, 381840]\) | \(11696828/7203\) | \(-1091893768670208\) | \([2]\) | \(788480\) | \(1.5747\) |
Rank
sage: E.rank()
The elliptic curves in class 177744da have rank \(0\).
Complex multiplication
The elliptic curves in class 177744da do not have complex multiplication.Modular form 177744.2.a.da
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.
