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SageMath
E = EllipticCurve("fa1")
E.isogeny_class()
Elliptic curves in class 115920.fa
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.fa1 | 115920fc1 | \([0, 0, 0, -23427, -1379646]\) | \(476196576129/197225\) | \(588910694400\) | \([2]\) | \(294912\) | \(1.2204\) | \(\Gamma_0(N)\)-optimal |
| 115920.fa2 | 115920fc2 | \([0, 0, 0, -19827, -1818126]\) | \(-288673724529/311181605\) | \(-929183293624320\) | \([2]\) | \(589824\) | \(1.5670\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.fa have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.fa do not have complex multiplication.Modular form 115920.2.a.fa
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.
