Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 6498.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6498.y1 | 6498x2 | \([1, -1, 1, -227498, -46176001]\) | \(-37966934881/4952198\) | \(-169842797473603302\) | \([]\) | \(108000\) | \(2.0393\) | |
6498.y2 | 6498x1 | \([1, -1, 1, -68, 219719]\) | \(-1/608\) | \(-20852239927392\) | \([]\) | \(21600\) | \(1.2346\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 6498.y have rank \(0\).
Complex multiplication
The elliptic curves in class 6498.y do not have complex multiplication.Modular form 6498.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.