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SageMath
E = EllipticCurve("hz1")
E.isogeny_class()
Elliptic curves in class 129360.hz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.hz1 | 129360di1 | \([0, 1, 0, -6435, 196020]\) | \(15657723904/49005\) | \(92246227920\) | \([2]\) | \(184320\) | \(0.97136\) | \(\Gamma_0(N)\)-optimal |
| 129360.hz2 | 129360di2 | \([0, 1, 0, -3740, 364188]\) | \(-192143824/1804275\) | \(-54341414265600\) | \([2]\) | \(368640\) | \(1.3179\) |
Rank
sage: E.rank()
The elliptic curves in class 129360.hz have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.hz do not have complex multiplication.Modular form 129360.2.a.hz
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.
