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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 61200.fu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61200.fu1 | 61200et2 | \([0, 0, 0, -23907675, -46444661750]\) | \(-32391289681150609/1228250000000\) | \(-57305232000000000000000\) | \([]\) | \(4354560\) | \(3.1369\) | |
| 61200.fu2 | 61200et1 | \([0, 0, 0, 1436325, -205685750]\) | \(7023836099951/4456448000\) | \(-207920037888000000000\) | \([]\) | \(1451520\) | \(2.5876\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 61200.fu have rank \(1\).
Complex multiplication
The elliptic curves in class 61200.fu do not have complex multiplication.Modular form 61200.2.a.fu
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.
