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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 111600.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111600.j1 | 111600cm1 | \([0, 0, 0, -19275, -2207750]\) | \(-458314011/953312\) | \(-1647323136000000\) | \([]\) | \(622080\) | \(1.6089\) | \(\Gamma_0(N)\)-optimal |
| 111600.j2 | 111600cm2 | \([0, 0, 0, 166725, 47702250]\) | \(406869021/1015808\) | \(-1279625527296000000\) | \([]\) | \(1866240\) | \(2.1583\) |
Rank
sage: E.rank()
The elliptic curves in class 111600.j have rank \(0\).
Complex multiplication
The elliptic curves in class 111600.j do not have complex multiplication.Modular form 111600.2.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.
