Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 47096.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47096.d1 | 47096c1 | \([0, 1, 0, -6167, -60770]\) | \(2725888/1421\) | \(13523903026256\) | \([2]\) | \(94080\) | \(1.2115\) | \(\Gamma_0(N)\)-optimal |
| 47096.d2 | 47096c2 | \([0, 1, 0, 23268, -449312]\) | \(9148592/5887\) | \(-896441572026112\) | \([2]\) | \(188160\) | \(1.5581\) |
Rank
sage: E.rank()
The elliptic curves in class 47096.d have rank \(1\).
Complex multiplication
The elliptic curves in class 47096.d do not have complex multiplication.Modular form 47096.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
