Show commands:
SageMath
E = EllipticCurve("fn1")
E.isogeny_class()
Elliptic curves in class 179520.fn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 179520.fn1 | 179520bq1 | \([0, 1, 0, -6561, -210465]\) | \(-119168121961/2524500\) | \(-661782528000\) | \([]\) | \(276480\) | \(1.0586\) | \(\Gamma_0(N)\)-optimal |
| 179520.fn2 | 179520bq2 | \([0, 1, 0, 27039, -929505]\) | \(8339492177639/6277634880\) | \(-1645644317982720\) | \([]\) | \(829440\) | \(1.6079\) |
Rank
sage: E.rank()
The elliptic curves in class 179520.fn have rank \(1\).
Complex multiplication
The elliptic curves in class 179520.fn do not have complex multiplication.Modular form 179520.2.a.fn
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
