Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 101150.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101150.ba1 | 101150s2 | \([1, 0, 1, -13156, -817172]\) | \(-417267265/235298\) | \(-141988042764050\) | \([]\) | \(362880\) | \(1.4187\) | |
101150.ba2 | 101150s1 | \([1, 0, 1, 1294, 15148]\) | \(397535/392\) | \(-236548176200\) | \([]\) | \(120960\) | \(0.86944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 101150.ba have rank \(0\).
Complex multiplication
The elliptic curves in class 101150.ba do not have complex multiplication.Modular form 101150.2.a.ba
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.