Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 120384.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 120384.d1 | 120384g2 | \([0, 0, 0, -107244, -13540176]\) | \(-26436959739/50578\) | \(-260971370643456\) | \([]\) | \(829440\) | \(1.6558\) | |
| 120384.d2 | 120384g1 | \([0, 0, 0, 2196, -91216]\) | \(165469149/603592\) | \(-4272156573696\) | \([]\) | \(276480\) | \(1.1065\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 120384.d have rank \(0\).
Complex multiplication
The elliptic curves in class 120384.d do not have complex multiplication.Modular form 120384.2.a.d
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.
