Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 1914.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1914.p1 | 1914p1 | \([1, 0, 0, -217350, 38984004]\) | \(-1135540872025530818401/1611210069216\) | \(-1611210069216\) | \([5]\) | \(10800\) | \(1.6141\) | \(\Gamma_0(N)\)-optimal |
1914.p2 | 1914p2 | \([1, 0, 0, 540540, 207657054]\) | \(17466551704682106586559/28728344556038333646\) | \(-28728344556038333646\) | \([]\) | \(54000\) | \(2.4188\) |
Rank
sage: E.rank()
The elliptic curves in class 1914.p have rank \(0\).
Complex multiplication
The elliptic curves in class 1914.p do not have complex multiplication.Modular form 1914.2.a.p
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.