Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 320.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 320.f1 | 320c3 | \([0, -1, 0, -165, -763]\) | \(488095744/125\) | \(128000\) | \([2]\) | \(48\) | \(-0.034070\) | |
| 320.f2 | 320c4 | \([0, -1, 0, -145, -975]\) | \(-20720464/15625\) | \(-256000000\) | \([2]\) | \(96\) | \(0.31250\) | |
| 320.f3 | 320c1 | \([0, -1, 0, -5, 5]\) | \(16384/5\) | \(5120\) | \([2]\) | \(16\) | \(-0.58338\) | \(\Gamma_0(N)\)-optimal |
| 320.f4 | 320c2 | \([0, -1, 0, 15, 17]\) | \(21296/25\) | \(-409600\) | \([2]\) | \(32\) | \(-0.23680\) |
Rank
sage: E.rank()
The elliptic curves in class 320.f have rank \(0\).
Complex multiplication
The elliptic curves in class 320.f do not have complex multiplication.Modular form 320.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
