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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 18480d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18480.f4 | 18480d1 | \([0, -1, 0, 44, 256]\) | \(35969456/144375\) | \(-36960000\) | \([2]\) | \(5120\) | \(0.13479\) | \(\Gamma_0(N)\)-optimal |
| 18480.f3 | 18480d2 | \([0, -1, 0, -456, 3456]\) | \(10262905636/1334025\) | \(1366041600\) | \([2, 2]\) | \(10240\) | \(0.48136\) | |
| 18480.f2 | 18480d3 | \([0, -1, 0, -1856, -26784]\) | \(345431270018/41507235\) | \(85006817280\) | \([2]\) | \(20480\) | \(0.82794\) | |
| 18480.f1 | 18480d4 | \([0, -1, 0, -7056, 230496]\) | \(18972782339618/396165\) | \(811345920\) | \([2]\) | \(20480\) | \(0.82794\) |
Rank
sage: E.rank()
The elliptic curves in class 18480d have rank \(2\).
Complex multiplication
The elliptic curves in class 18480d do not have complex multiplication.Modular form 18480.2.a.d
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.
