Show commands:
SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 152880.n
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.n1 | 152880hu1 | \([0, -1, 0, -891, -1770]\) | \(14270199808/7921875\) | \(43475250000\) | \([2]\) | \(110592\) | \(0.73170\) | \(\Gamma_0(N)\)-optimal |
| 152880.n2 | 152880hu2 | \([0, -1, 0, 3484, -17520]\) | \(53247522512/32131125\) | \(-2821369824000\) | \([2]\) | \(221184\) | \(1.0783\) |
Rank
sage: E.rank()
The elliptic curves in class 152880.n have rank \(1\).
Complex multiplication
The elliptic curves in class 152880.n do not have complex multiplication.Modular form 152880.2.a.n
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.
