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SageMath
E = EllipticCurve("et1")
E.isogeny_class()
Elliptic curves in class 121968.et
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121968.et1 | 121968g2 | \([0, 0, 0, -120879, -16171650]\) | \(21882096/7\) | \(62486386212096\) | \([2]\) | \(537600\) | \(1.6220\) | |
| 121968.et2 | 121968g1 | \([0, 0, 0, -6534, -323433]\) | \(-55296/49\) | \(-27337793967792\) | \([2]\) | \(268800\) | \(1.2754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 121968.et have rank \(0\).
Complex multiplication
The elliptic curves in class 121968.et do not have complex multiplication.Modular form 121968.2.a.et
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.
