Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 23520.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.f1 | 23520c1 | \([0, -1, 0, -1486, -19424]\) | \(140608/15\) | \(38739462720\) | \([2]\) | \(17920\) | \(0.76604\) | \(\Gamma_0(N)\)-optimal |
| 23520.f2 | 23520c2 | \([0, -1, 0, 1944, -99000]\) | \(39304/225\) | \(-4648735526400\) | \([2]\) | \(35840\) | \(1.1126\) |
Rank
sage: E.rank()
The elliptic curves in class 23520.f have rank \(0\).
Complex multiplication
The elliptic curves in class 23520.f do not have complex multiplication.Modular form 23520.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
