Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 469336a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 469336.a1 | 469336a1 | \([0, 1, 0, -2119, -12534]\) | \(2725888/1421\) | \(548791768784\) | \([2]\) | \(551936\) | \(0.94443\) | \(\Gamma_0(N)\)-optimal |
| 469336.a2 | 469336a2 | \([0, 1, 0, 7996, -89408]\) | \(9148592/5887\) | \(-36377054387968\) | \([2]\) | \(1103872\) | \(1.2910\) |
Rank
sage: E.rank()
The elliptic curves in class 469336a have rank \(0\).
Complex multiplication
The elliptic curves in class 469336a do not have complex multiplication.Modular form 469336.2.a.a
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 Cremona 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 Cremona labels.
