Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 97461.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
97461.x1 | 97461c1 | \([1, -1, 0, -2293650, -1336276537]\) | \(420100556152674123/62939003491\) | \(199927192186241793\) | \([2]\) | \(2211840\) | \(2.3330\) | \(\Gamma_0(N)\)-optimal |
97461.x2 | 97461c2 | \([1, -1, 0, -2081235, -1593935932]\) | \(-313859434290315003/164114213839849\) | \(-521312574889198665027\) | \([2]\) | \(4423680\) | \(2.6796\) |
Rank
sage: E.rank()
The elliptic curves in class 97461.x have rank \(0\).
Complex multiplication
The elliptic curves in class 97461.x do not have complex multiplication.Modular form 97461.2.a.x
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.