Show commands:
SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 111090.bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.bs1 | 111090bs1 | \([1, 1, 1, -129616, -17200591]\) | \(1626794704081/83462400\) | \(12355430582073600\) | \([2]\) | \(1622016\) | \(1.8456\) | \(\Gamma_0(N)\)-optimal |
111090.bs2 | 111090bs2 | \([1, 1, 1, 81984, -67646031]\) | \(411664745519/13605414480\) | \(-2014089627760272720\) | \([2]\) | \(3244032\) | \(2.1922\) |
Rank
sage: E.rank()
The elliptic curves in class 111090.bs have rank \(1\).
Complex multiplication
The elliptic curves in class 111090.bs do not have complex multiplication.Modular form 111090.2.a.bs
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.