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SageMath
E = EllipticCurve("fs1")
E.isogeny_class()
Elliptic curves in class 162624.fs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162624.fs1 | 162624i2 | \([0, 1, 0, -189889, 26372927]\) | \(2450086/441\) | \(136295865611845632\) | \([2]\) | \(1351680\) | \(2.0069\) | |
| 162624.fs2 | 162624i1 | \([0, 1, 0, 23071, 2393631]\) | \(8788/21\) | \(-3245139657424896\) | \([2]\) | \(675840\) | \(1.6603\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162624.fs have rank \(0\).
Complex multiplication
The elliptic curves in class 162624.fs do not have complex multiplication.Modular form 162624.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
