Show commands:
SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 45504.bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45504.bl1 | 45504br2 | \([0, 0, 0, -13466892, -19021121008]\) | \(1413378216646643521/49232902384\) | \(9408554162699894784\) | \([]\) | \(1382400\) | \(2.7311\) | |
| 45504.bl2 | 45504br1 | \([0, 0, 0, -241932, 45400592]\) | \(8194759433281/82837504\) | \(15830493538811904\) | \([]\) | \(276480\) | \(1.9264\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 45504.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 45504.bl do not have complex multiplication.Modular form 45504.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
