Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 29645.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29645.j1 | 29645a2 | \([1, -1, 0, -395390, -91393219]\) | \(24642171/1225\) | \(339827480175612275\) | \([2]\) | \(304128\) | \(2.1229\) | |
| 29645.j2 | 29645a1 | \([1, -1, 0, -69295, 5196120]\) | \(132651/35\) | \(9709356576446065\) | \([2]\) | \(152064\) | \(1.7763\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29645.j have rank \(0\).
Complex multiplication
The elliptic curves in class 29645.j do not have complex multiplication.Modular form 29645.2.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.
