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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 32760.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32760.z1 | 32760y2 | \([0, 0, 0, -9892347, 11970756086]\) | \(1936101054887046531846/905403781953125\) | \(50065207526880000000\) | \([2]\) | \(1333248\) | \(2.7360\) | |
| 32760.z2 | 32760y1 | \([0, 0, 0, -517347, 250131086]\) | \(-553867390580563692/657061767578125\) | \(-18166443750000000000\) | \([2]\) | \(666624\) | \(2.3894\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32760.z have rank \(1\).
Complex multiplication
The elliptic curves in class 32760.z do not have complex multiplication.Modular form 32760.2.a.z
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.
