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SageMath
E = EllipticCurve("fq1")
E.isogeny_class()
Elliptic curves in class 224400.fq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.fq1 | 224400bq2 | \([0, 1, 0, -4704008, -3926208012]\) | \(179865548102096641/119964240000\) | \(7677711360000000000\) | \([2]\) | \(6193152\) | \(2.5625\) | |
| 224400.fq2 | 224400bq1 | \([0, 1, 0, -352008, -35520012]\) | \(75370704203521/35157196800\) | \(2250060595200000000\) | \([2]\) | \(3096576\) | \(2.2159\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 224400.fq have rank \(0\).
Complex multiplication
The elliptic curves in class 224400.fq do not have complex multiplication.Modular form 224400.2.a.fq
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.
