Show commands:
SageMath
E = EllipticCurve("jq1")
E.isogeny_class()
Elliptic curves in class 346560.jq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
346560.jq1 | 346560jq1 | \([0, 1, 0, -2305, -49825]\) | \(-14317849/2700\) | \(-255511756800\) | \([]\) | \(497664\) | \(0.91300\) | \(\Gamma_0(N)\)-optimal |
346560.jq2 | 346560jq2 | \([0, 1, 0, 15935, 245663]\) | \(4728305591/3000000\) | \(-283901952000000\) | \([]\) | \(1492992\) | \(1.4623\) |
Rank
sage: E.rank()
The elliptic curves in class 346560.jq have rank \(0\).
Complex multiplication
The elliptic curves in class 346560.jq do not have complex multiplication.Modular form 346560.2.a.jq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.