Show commands:
SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 369600.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 369600.fe1 | 369600fe2 | \([0, -1, 0, -3547633, -2082282863]\) | \(19288565375865424/3837216796875\) | \(982327500000000000000\) | \([2]\) | \(13271040\) | \(2.7443\) | |
| 369600.fe2 | 369600fe1 | \([0, -1, 0, 461867, -193808363]\) | \(681010157060096/1406657896875\) | \(-22506526350000000000\) | \([2]\) | \(6635520\) | \(2.3977\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 369600.fe have rank \(0\).
Complex multiplication
The elliptic curves in class 369600.fe do not have complex multiplication.Modular form 369600.2.a.fe
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.
