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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 304200.fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 304200.fv1 | 304200fv2 | \([0, 0, 0, -2596359675, 50879300845750]\) | \(7824392006186/7381125\) | \(1825955703416823732000000000\) | \([2]\) | \(287539200\) | \(4.1532\) | |
| 304200.fv2 | 304200fv1 | \([0, 0, 0, -124734675, 1172450470750]\) | \(-1735192372/3796875\) | \(-469638812607207750000000000\) | \([2]\) | \(143769600\) | \(3.8066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 304200.fv have rank \(0\).
Complex multiplication
The elliptic curves in class 304200.fv do not have complex multiplication.Modular form 304200.2.a.fv
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.
