Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 122304.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122304.s1 | 122304bc2 | \([0, -1, 0, -2809, 46873]\) | \(5088448/1053\) | \(507430490112\) | \([2]\) | \(184320\) | \(0.96123\) | |
122304.s2 | 122304bc1 | \([0, -1, 0, 376, 4194]\) | \(778688/1521\) | \(-11452424256\) | \([2]\) | \(92160\) | \(0.61466\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 122304.s have rank \(0\).
Complex multiplication
The elliptic curves in class 122304.s do not have complex multiplication.Modular form 122304.2.a.s
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.