Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 32368.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32368.ba1 | 32368x2 | \([0, 1, 0, -708, 7016]\) | \(531250000/343\) | \(25376512\) | \([]\) | \(10368\) | \(0.36108\) | |
| 32368.ba2 | 32368x1 | \([0, 1, 0, -28, -56]\) | \(34000/7\) | \(517888\) | \([]\) | \(3456\) | \(-0.18822\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32368.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 32368.ba do not have complex multiplication.Modular form 32368.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
