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SageMath
E = EllipticCurve("ga1")
E.isogeny_class()
Elliptic curves in class 54450.ga
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54450.ga1 | 54450fh2 | \([1, -1, 1, -607685, 182484987]\) | \(6352571665/2\) | \(7813381212450\) | \([]\) | \(456192\) | \(1.8355\) | |
54450.ga2 | 54450fh1 | \([1, -1, 1, -8735, 164607]\) | \(18865/8\) | \(31253524849800\) | \([]\) | \(152064\) | \(1.2861\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54450.ga have rank \(0\).
Complex multiplication
The elliptic curves in class 54450.ga do not have complex multiplication.Modular form 54450.2.a.ga
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.