Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2898j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2898.j2 | 2898j1 | \([1, -1, 0, 27, -243]\) | \(2924207/34776\) | \(-25351704\) | \([]\) | \(960\) | \(0.10160\) | \(\Gamma_0(N)\)-optimal |
2898.j1 | 2898j2 | \([1, -1, 0, -243, 6723]\) | \(-2181825073/25039686\) | \(-18253931094\) | \([3]\) | \(2880\) | \(0.65091\) |
Rank
sage: E.rank()
The elliptic curves in class 2898j have rank \(0\).
Complex multiplication
The elliptic curves in class 2898j do not have complex multiplication.Modular form 2898.2.a.j
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 Cremona 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 Cremona labels.