Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 81144.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81144.y1 | 81144bn2 | \([0, 0, 0, -215355, 38463334]\) | \(12576878500/1127\) | \(98978220407808\) | \([2]\) | \(368640\) | \(1.7255\) | |
81144.y2 | 81144bn1 | \([0, 0, 0, -12495, 690802]\) | \(-9826000/3703\) | \(-81303538192128\) | \([2]\) | \(184320\) | \(1.3789\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 81144.y have rank \(2\).
Complex multiplication
The elliptic curves in class 81144.y do not have complex multiplication.Modular form 81144.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.