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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 298816.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 298816.cf1 | 298816cf2 | \([0, -1, 0, -34657, -2269215]\) | \(17561807821657/1590616244\) | \(416970504667136\) | \([2]\) | \(983040\) | \(1.5448\) | |
| 298816.cf2 | 298816cf1 | \([0, -1, 0, 2463, -168223]\) | \(6300872423/49827568\) | \(-13061997985792\) | \([2]\) | \(491520\) | \(1.1982\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 298816.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 298816.cf do not have complex multiplication.Modular form 298816.2.a.cf
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
