Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 141.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141.b1 | 141b2 | \([1, 1, 1, -143, -718]\) | \(323535264625/59643\) | \(59643\) | \([2]\) | \(24\) | \(-0.081025\) | |
141.b2 | 141b1 | \([1, 1, 1, -8, -16]\) | \(-57066625/34263\) | \(-34263\) | \([2]\) | \(12\) | \(-0.42760\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141.b have rank \(0\).
Complex multiplication
The elliptic curves in class 141.b do not have complex multiplication.Modular form 141.2.a.b
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.