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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 29232.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29232.y1 | 29232bi2 | \([0, 0, 0, -64875, 1416602]\) | \(10112728515625/5561943408\) | \(16607874025193472\) | \([2]\) | \(122880\) | \(1.8030\) | |
29232.y2 | 29232bi1 | \([0, 0, 0, 15765, 174746]\) | \(145116956375/88397568\) | \(-263953723686912\) | \([2]\) | \(61440\) | \(1.4564\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29232.y have rank \(0\).
Complex multiplication
The elliptic curves in class 29232.y do not have complex multiplication.Modular form 29232.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.