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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 33462j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33462.x2 | 33462j1 | \([1, -1, 0, -201057, -33107203]\) | \(9460870875/475904\) | \(45213774232543488\) | \([2]\) | \(258048\) | \(1.9544\) | \(\Gamma_0(N)\)-optimal |
| 33462.x1 | 33462j2 | \([1, -1, 0, -566097, 121450733]\) | \(211176358875/55294096\) | \(5253275393643646512\) | \([2]\) | \(516096\) | \(2.3010\) |
Rank
sage: E.rank()
The elliptic curves in class 33462j have rank \(0\).
Complex multiplication
The elliptic curves in class 33462j do not have complex multiplication.Modular form 33462.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
