Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 63580.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 63580.j1 | 63580b1 | \([0, 1, 0, -28996, 1890820]\) | \(-126100646224/605\) | \(-12935732480\) | \([3]\) | \(88128\) | \(1.1413\) | \(\Gamma_0(N)\)-optimal |
| 63580.j2 | 63580b2 | \([0, 1, 0, -17436, 3421364]\) | \(-27419122384/221445125\) | \(-4734801480992000\) | \([]\) | \(264384\) | \(1.6906\) |
Rank
sage: E.rank()
The elliptic curves in class 63580.j have rank \(1\).
Complex multiplication
The elliptic curves in class 63580.j do not have complex multiplication.Modular form 63580.2.a.j
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.
