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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 486720.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
486720.q1 | 486720q2 | \([0, 0, 0, -2030028, -1063383152]\) | \(12326391/625\) | \(46910911786352640000\) | \([2]\) | \(15335424\) | \(2.5328\) | \(\Gamma_0(N)\)-optimal* |
486720.q2 | 486720q1 | \([0, 0, 0, 79092, -65347568]\) | \(729/25\) | \(-1876436471454105600\) | \([2]\) | \(7667712\) | \(2.1863\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 486720.q have rank \(1\).
Complex multiplication
The elliptic curves in class 486720.q do not have complex multiplication.Modular form 486720.2.a.q
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.