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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 159936.gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 159936.gh1 | 159936fo2 | \([0, 1, 0, -1194097, 501680591]\) | \(40685771728/14739\) | \(68213189755060224\) | \([]\) | \(3773952\) | \(2.1987\) | |
| 159936.gh2 | 159936fo1 | \([0, 1, 0, -41617, -2414161]\) | \(1722448/459\) | \(2124286186143744\) | \([]\) | \(1257984\) | \(1.6494\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 159936.gh have rank \(0\).
Complex multiplication
The elliptic curves in class 159936.gh do not have complex multiplication.Modular form 159936.2.a.gh
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.
