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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 67280.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 67280.x1 | 67280u2 | \([0, -1, 0, -720176, 205760960]\) | \(14258975033569/1953125000\) | \(5658248000000000000\) | \([]\) | \(933120\) | \(2.3252\) | |
| 67280.x2 | 67280u1 | \([0, -1, 0, -181936, -29772864]\) | \(229895296609/320000\) | \(927047352320000\) | \([]\) | \(311040\) | \(1.7759\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67280.x have rank \(1\).
Complex multiplication
The elliptic curves in class 67280.x do not have complex multiplication.Modular form 67280.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
