Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 72600.bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72600.bn1 | 72600c1 | \([0, -1, 0, -20752508, 36394005012]\) | \(104795188976/1875\) | \(17684607682500000000\) | \([2]\) | \(4055040\) | \(2.8202\) | \(\Gamma_0(N)\)-optimal |
| 72600.bn2 | 72600c2 | \([0, -1, 0, -20087008, 38836390012]\) | \(-23758298924/3515625\) | \(-132634557618750000000000\) | \([2]\) | \(8110080\) | \(3.1668\) |
Rank
sage: E.rank()
The elliptic curves in class 72600.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 72600.bn do not have complex multiplication.Modular form 72600.2.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 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.
