Show commands:
SageMath
E = EllipticCurve("pm1")
E.isogeny_class()
Elliptic curves in class 141120.pm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.pm1 | 141120gp1 | \([0, 0, 0, -5292, -71344]\) | \(78732/35\) | \(7286181396480\) | \([2]\) | \(294912\) | \(1.1637\) | \(\Gamma_0(N)\)-optimal |
141120.pm2 | 141120gp2 | \([0, 0, 0, 18228, -532336]\) | \(1608714/1225\) | \(-510032697753600\) | \([2]\) | \(589824\) | \(1.5102\) |
Rank
sage: E.rank()
The elliptic curves in class 141120.pm have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.pm do not have complex multiplication.Modular form 141120.2.a.pm
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.