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SageMath
E = EllipticCurve("fc1")
E.isogeny_class()
Elliptic curves in class 80850.fc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 80850.fc1 | 80850ff2 | \([1, 1, 1, -343638, 9854781]\) | \(19530306557/11114334\) | \(2553887267121093750\) | \([2]\) | \(1474560\) | \(2.2219\) | |
| 80850.fc2 | 80850ff1 | \([1, 1, 1, 85112, 1279781]\) | \(296740963/174636\) | \(-40128419460937500\) | \([2]\) | \(737280\) | \(1.8753\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 80850.fc have rank \(1\).
Complex multiplication
The elliptic curves in class 80850.fc do not have complex multiplication.Modular form 80850.2.a.fc
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.
