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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 36225.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 36225.v1 | 36225bo4 | \([1, -1, 1, -996755, 382082622]\) | \(9614816895690721/34652610405\) | \(394714890394453125\) | \([2]\) | \(393216\) | \(2.2376\) | |
| 36225.v2 | 36225bo2 | \([1, -1, 1, -91130, -91128]\) | \(7347774183121/4251692025\) | \(48429429472265625\) | \([2, 2]\) | \(196608\) | \(1.8910\) | |
| 36225.v3 | 36225bo1 | \([1, -1, 1, -63005, -6053628]\) | \(2428257525121/8150625\) | \(92840712890625\) | \([2]\) | \(98304\) | \(1.5445\) | \(\Gamma_0(N)\)-optimal |
| 36225.v4 | 36225bo3 | \([1, -1, 1, 364495, -1002378]\) | \(470166844956479/272118787605\) | \(-3099603065063203125\) | \([2]\) | \(393216\) | \(2.2376\) |
Rank
sage: E.rank()
The elliptic curves in class 36225.v have rank \(1\).
Complex multiplication
The elliptic curves in class 36225.v do not have complex multiplication.Modular form 36225.2.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 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.
