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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 22320ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22320.by2 | 22320ce1 | \([0, 0, 0, -5907, -179246]\) | \(-7633736209/230640\) | \(-688687349760\) | \([2]\) | \(30720\) | \(1.0493\) | \(\Gamma_0(N)\)-optimal |
| 22320.by1 | 22320ce2 | \([0, 0, 0, -95187, -11303534]\) | \(31942518433489/27900\) | \(83308953600\) | \([2]\) | \(61440\) | \(1.3959\) |
Rank
sage: E.rank()
The elliptic curves in class 22320ce have rank \(1\).
Complex multiplication
The elliptic curves in class 22320ce do not have complex multiplication.Modular form 22320.2.a.ce
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.
