Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 238425bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 238425.bn1 | 238425bn1 | \([0, 1, 1, -6743, 221339]\) | \(-56197120/3267\) | \(-1971435948075\) | \([]\) | \(331776\) | \(1.1154\) | \(\Gamma_0(N)\)-optimal |
| 238425.bn2 | 238425bn2 | \([0, 1, 1, 36607, 407744]\) | \(8990228480/5314683\) | \(-3207088190640675\) | \([]\) | \(995328\) | \(1.6647\) |
Rank
sage: E.rank()
The elliptic curves in class 238425bn have rank \(1\).
Complex multiplication
The elliptic curves in class 238425bn do not have complex multiplication.Modular form 238425.2.a.bn
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 Cremona 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 Cremona labels.
