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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 29232.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29232.b1 | 29232bw2 | \([0, 0, 0, -1051347, 414915730]\) | \(43040219271568849/841158108\) | \(2511684651958272\) | \([2]\) | \(331776\) | \(2.0770\) | |
| 29232.b2 | 29232bw1 | \([0, 0, 0, -63507, 6937810]\) | \(-9486391169809/1473906672\) | \(-4401061740085248\) | \([2]\) | \(165888\) | \(1.7305\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29232.b have rank \(1\).
Complex multiplication
The elliptic curves in class 29232.b do not have complex multiplication.Modular form 29232.2.a.b
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.
