Show commands:
SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 101430.db
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.db1 | 101430da1 | \([1, -1, 1, -562358, -159091019]\) | \(8493409990827/185150000\) | \(428749127185050000\) | \([2]\) | \(1474560\) | \(2.1716\) | \(\Gamma_0(N)\)-optimal |
101430.db2 | 101430da2 | \([1, -1, 1, 46222, -485776763]\) | \(4716275733/44023437500\) | \(-101944425621445312500\) | \([2]\) | \(2949120\) | \(2.5182\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.db have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.db do not have complex multiplication.Modular form 101430.2.a.db
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.