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SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 162288.fs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162288.fs1 | 162288el1 | \([0, 0, 0, -8754291, 9969642802]\) | \(-5702623460245179/252448\) | \(-3284610573533184\) | \([]\) | \(6082560\) | \(2.4594\) | \(\Gamma_0(N)\)-optimal |
| 162288.fs2 | 162288el2 | \([0, 0, 0, -8013411, 11726444898]\) | \(-5999796014211/2790817792\) | \(-26471037517069805420544\) | \([]\) | \(18247680\) | \(3.0087\) |
Rank
sage: E.rank()
The elliptic curves in class 162288.fs have rank \(0\).
Complex multiplication
The elliptic curves in class 162288.fs do not have complex multiplication.Modular form 162288.2.a.fs
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.
