Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 15600.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15600.z1 | 15600i2 | \([0, -1, 0, -107008, 9476512]\) | \(4234737878642/1247410125\) | \(39917124000000000\) | \([2]\) | \(92160\) | \(1.8913\) | |
| 15600.z2 | 15600i1 | \([0, -1, 0, 17992, 976512]\) | \(40254822716/49359375\) | \(-789750000000000\) | \([2]\) | \(46080\) | \(1.5447\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15600.z have rank \(0\).
Complex multiplication
The elliptic curves in class 15600.z do not have complex multiplication.Modular form 15600.2.a.z
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.
