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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 116032.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116032.q1 | 116032bb3 | \([0, -1, 0, -367173, -85513301]\) | \(727057727488000/37\) | \(278592832\) | \([]\) | \(326592\) | \(1.5416\) | |
| 116032.q2 | 116032bb2 | \([0, -1, 0, -4573, -113749]\) | \(1404928000/50653\) | \(381393587008\) | \([]\) | \(108864\) | \(0.99230\) | |
| 116032.q3 | 116032bb1 | \([0, -1, 0, -653, 6595]\) | \(4096000/37\) | \(278592832\) | \([]\) | \(36288\) | \(0.44300\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 116032.q have rank \(1\).
Complex multiplication
The elliptic curves in class 116032.q do not have complex multiplication.Modular form 116032.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
