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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 297024v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 297024.v1 | 297024v1 | \([0, -1, 0, -1020510849, -8694675273087]\) | \(448370126000857162602152353/134883063988931602326528\) | \(35358785926314485960285356032\) | \([2]\) | \(309657600\) | \(4.1832\) | \(\Gamma_0(N)\)-optimal |
| 297024.v2 | 297024v2 | \([0, -1, 0, 2781529471, -58258833292671]\) | \(9078932501639240351982661727/10847124527712371223290784\) | \(-2843508612192631841958339280896\) | \([2]\) | \(619315200\) | \(4.5298\) |
Rank
sage: E.rank()
The elliptic curves in class 297024v have rank \(1\).
Complex multiplication
The elliptic curves in class 297024v do not have complex multiplication.Modular form 297024.2.a.v
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 Cremona 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 Cremona labels.
