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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 31200ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
31200.bk2 | 31200ba1 | \([0, 1, 0, -198, 1008]\) | \(107850176/117\) | \(936000\) | \([2]\) | \(7168\) | \(0.061373\) | \(\Gamma_0(N)\)-optimal |
31200.bk1 | 31200ba2 | \([0, 1, 0, -248, 408]\) | \(26463592/13689\) | \(876096000\) | \([2]\) | \(14336\) | \(0.40795\) |
Rank
sage: E.rank()
The elliptic curves in class 31200ba have rank \(1\).
Complex multiplication
The elliptic curves in class 31200ba do not have complex multiplication.Modular form 31200.2.a.ba
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.