Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 20339f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20339.f3 | 20339f1 | \([0, 1, 1, -616, -14193]\) | \(-4096/11\) | \(-69534993539\) | \([]\) | \(15960\) | \(0.76787\) | \(\Gamma_0(N)\)-optimal |
| 20339.f2 | 20339f2 | \([0, 1, 1, -19106, 1834807]\) | \(-122023936/161051\) | \(-1018061840404499\) | \([]\) | \(79800\) | \(1.5726\) | |
| 20339.f1 | 20339f3 | \([0, 1, 1, -14459796, 21158869387]\) | \(-52893159101157376/11\) | \(-69534993539\) | \([]\) | \(399000\) | \(2.3773\) |
Rank
sage: E.rank()
The elliptic curves in class 20339f have rank \(1\).
Complex multiplication
The elliptic curves in class 20339f do not have complex multiplication.Modular form 20339.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
