Show commands:
SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 188760.cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.cu1 | 188760k2 | \([0, 1, 0, -24240, -1438560]\) | \(434163602/7605\) | \(27592133437440\) | \([2]\) | \(552960\) | \(1.3756\) | |
188760.cu2 | 188760k1 | \([0, 1, 0, -40, -64000]\) | \(-4/975\) | \(-1768726502400\) | \([2]\) | \(276480\) | \(1.0290\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 188760.cu have rank \(1\).
Complex multiplication
The elliptic curves in class 188760.cu do not have complex multiplication.Modular form 188760.2.a.cu
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.