Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 148800.by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
148800.by1 | 148800en2 | \([0, -1, 0, -836033, 294563937]\) | \(-15777367606441/3574920\) | \(-14642872320000000\) | \([]\) | \(1658880\) | \(2.0940\) | |
148800.by2 | 148800en1 | \([0, -1, 0, 3967, 1403937]\) | \(1685159/209250\) | \(-857088000000000\) | \([]\) | \(552960\) | \(1.5447\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 148800.by have rank \(0\).
Complex multiplication
The elliptic curves in class 148800.by do not have complex multiplication.Modular form 148800.2.a.by
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.