Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 226512.cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
226512.cj1 | 226512ey1 | \([0, 0, 0, -3630, 38599]\) | \(256000/117\) | \(2417628037968\) | \([2]\) | \(358400\) | \(1.0711\) | \(\Gamma_0(N)\)-optimal |
226512.cj2 | 226512ey2 | \([0, 0, 0, 12705, 290158]\) | \(686000/507\) | \(-167622210632448\) | \([2]\) | \(716800\) | \(1.4177\) |
Rank
sage: E.rank()
The elliptic curves in class 226512.cj have rank \(0\).
Complex multiplication
The elliptic curves in class 226512.cj do not have complex multiplication.Modular form 226512.2.a.cj
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.