Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 2254.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2254.g1 | 2254f2 | \([1, 1, 1, -8527, -306251]\) | \(582810602977/829472\) | \(97586551328\) | \([2]\) | \(3840\) | \(1.0116\) | |
2254.g2 | 2254f1 | \([1, 1, 1, -687, -2059]\) | \(304821217/164864\) | \(19396084736\) | \([2]\) | \(1920\) | \(0.66503\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2254.g have rank \(0\).
Complex multiplication
The elliptic curves in class 2254.g do not have complex multiplication.Modular form 2254.2.a.g
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.