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SageMath
E = EllipticCurve("da1")
E.isogeny_class()
Elliptic curves in class 377520.da
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.da1 | 377520da4 | \([0, -1, 0, -4397764400, -112251041982528]\) | \(1296294060988412126189641/647824320\) | \(4700816589469777920\) | \([2]\) | \(119439360\) | \(3.8190\) | |
| 377520.da2 | 377520da3 | \([0, -1, 0, -274858800, -1753873578048]\) | \(-316472948332146183241/7074906009600\) | \(-51337738507358149017600\) | \([2]\) | \(59719680\) | \(3.4724\) | |
| 377520.da3 | 377520da2 | \([0, -1, 0, -54396800, -153347336448]\) | \(2453170411237305241/19353090685500\) | \(140432100097618188288000\) | \([2]\) | \(39813120\) | \(3.2697\) | |
| 377520.da4 | 377520da1 | \([0, -1, 0, -1156800, -5510504448]\) | \(-23592983745241/1794399750000\) | \(-13020727769127936000000\) | \([2]\) | \(19906560\) | \(2.9231\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 377520.da have rank \(0\).
Complex multiplication
The elliptic curves in class 377520.da do not have complex multiplication.Modular form 377520.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
