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SageMath
E = EllipticCurve("fv1")
E.isogeny_class()
Elliptic curves in class 109200.fv
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 109200.fv1 | 109200gm2 | \([0, 1, 0, -1469798408, 21688272547188]\) | \(-5486773802537974663600129/2635437714\) | \(-168668013696000000\) | \([]\) | \(27659520\) | \(3.5444\) | |
| 109200.fv2 | 109200gm1 | \([0, 1, 0, 285592, 663835188]\) | \(40251338884511/2997011332224\) | \(-191808725262336000000\) | \([]\) | \(3951360\) | \(2.5715\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 109200.fv have rank \(1\).
Complex multiplication
The elliptic curves in class 109200.fv do not have complex multiplication.Modular form 109200.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
