Show commands:
SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 95550.co
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95550.co1 | 95550x2 | \([1, 1, 0, -56375, 4591875]\) | \(10779215329/1232010\) | \(2264761632656250\) | \([2]\) | \(829440\) | \(1.6786\) | |
95550.co2 | 95550x1 | \([1, 1, 0, 4875, 365625]\) | \(6967871/35100\) | \(-64523123437500\) | \([2]\) | \(414720\) | \(1.3321\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 95550.co have rank \(0\).
Complex multiplication
The elliptic curves in class 95550.co do not have complex multiplication.Modular form 95550.2.a.co
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.