Show commands:
SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 94864.cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94864.cw1 | 94864cr2 | \([0, -1, 0, -2847896, 1850854832]\) | \(-24729001\) | \(-103297466330189824\) | \([]\) | \(1520640\) | \(2.3471\) | |
94864.cw2 | 94864cr1 | \([0, -1, 0, -1976, -131536]\) | \(-121\) | \(-7055355940864\) | \([]\) | \(138240\) | \(1.1481\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 94864.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 94864.cw do not have complex multiplication.Modular form 94864.2.a.cw
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.