Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 329672.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 329672.ba1 | 329672ba1 | \([0, -1, 0, -302199, 20239724]\) | \(2725888/1421\) | \(1591073667135992144\) | \([2]\) | \(4515840\) | \(2.1844\) | \(\Gamma_0(N)\)-optimal |
| 329672.ba2 | 329672ba2 | \([0, -1, 0, 1140116, 156394260]\) | \(9148592/5887\) | \(-105465454507300050688\) | \([2]\) | \(9031680\) | \(2.5310\) |
Rank
sage: E.rank()
The elliptic curves in class 329672.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 329672.ba do not have complex multiplication.Modular form 329672.2.a.ba
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.
