Show commands:
SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 41280.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.m1 | 41280bw2 | \([0, -1, 0, -32481, 2263425]\) | \(14457238157881/4437600\) | \(1163290214400\) | \([2]\) | \(92160\) | \(1.2920\) | |
41280.m2 | 41280bw1 | \([0, -1, 0, -1761, 45441]\) | \(-2305199161/1981440\) | \(-519422607360\) | \([2]\) | \(46080\) | \(0.94547\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41280.m have rank \(0\).
Complex multiplication
The elliptic curves in class 41280.m do not have complex multiplication.Modular form 41280.2.a.m
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.