Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 48400.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48400.k1 | 48400bd2 | \([0, 1, 0, -27628, -1106052]\) | \(41141648/14641\) | \(829997587232000\) | \([2]\) | \(184320\) | \(1.5637\) | |
48400.k2 | 48400bd1 | \([0, 1, 0, -24603, -1493252]\) | \(464857088/121\) | \(428717762000\) | \([2]\) | \(92160\) | \(1.2171\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 48400.k have rank \(1\).
Complex multiplication
The elliptic curves in class 48400.k do not have complex multiplication.Modular form 48400.2.a.k
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.