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SageMath
E = EllipticCurve("qb1")
E.isogeny_class()
Elliptic curves in class 141120.qb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.qb1 | 141120kl1 | \([0, 0, 0, -1757532, 897359344]\) | \(-177953104/125\) | \(-421733286955008000\) | \([]\) | \(2903040\) | \(2.3182\) | \(\Gamma_0(N)\)-optimal |
| 141120.qb2 | 141120kl2 | \([0, 0, 0, 1699908, 3811289776]\) | \(161017136/1953125\) | \(-6589582608672000000000\) | \([]\) | \(8709120\) | \(2.8675\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.qb have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.qb do not have complex multiplication.Modular form 141120.2.a.qb
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.
