Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 88445.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88445.y1 | 88445bh2 | \([0, -1, 1, -5153395, 3354639413]\) | \(7575076864/1953125\) | \(3902537516036345703125\) | \([]\) | \(4136832\) | \(2.8523\) | |
88445.y2 | 88445bh1 | \([0, -1, 1, -1792485, -922790744]\) | \(318767104/125\) | \(249762401026326125\) | \([]\) | \(1378944\) | \(2.3029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 88445.y have rank \(1\).
Complex multiplication
The elliptic curves in class 88445.y do not have complex multiplication.Modular form 88445.2.a.y
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.