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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 9360.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9360.j1 | 9360i2 | \([0, 0, 0, -38523, -2039222]\) | \(4234737878642/1247410125\) | \(1862373337344000\) | \([2]\) | \(30720\) | \(1.6358\) | |
| 9360.j2 | 9360i1 | \([0, 0, 0, 6477, -212222]\) | \(40254822716/49359375\) | \(-36846576000000\) | \([2]\) | \(15360\) | \(1.2893\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9360.j have rank \(0\).
Complex multiplication
The elliptic curves in class 9360.j do not have complex multiplication.Modular form 9360.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
