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SageMath
E = EllipticCurve("ja1")
E.isogeny_class()
Elliptic curves in class 299200.ja
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
299200.ja1 | 299200ja1 | \([0, -1, 0, -1315533, -580327813]\) | \(-251784668965666816/353546875\) | \(-353546875000000\) | \([]\) | \(5059584\) | \(2.0639\) | \(\Gamma_0(N)\)-optimal |
299200.ja2 | 299200ja2 | \([0, -1, 0, -965533, -896202813]\) | \(-99546392709922816/289614925147075\) | \(-289614925147075000000\) | \([]\) | \(15178752\) | \(2.6132\) |
Rank
sage: E.rank()
The elliptic curves in class 299200.ja have rank \(1\).
Complex multiplication
The elliptic curves in class 299200.ja do not have complex multiplication.Modular form 299200.2.a.ja
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.