Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 5550.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.q1 | 5550o2 | \([1, 0, 1, -528651, -147949802]\) | \(1045706191321645729/323352324000\) | \(5052380062500000\) | \([2]\) | \(57600\) | \(1.9897\) | |
5550.q2 | 5550o1 | \([1, 0, 1, -28651, -2949802]\) | \(-166456688365729/143856000000\) | \(-2247750000000000\) | \([2]\) | \(28800\) | \(1.6431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5550.q have rank \(1\).
Complex multiplication
The elliptic curves in class 5550.q do not have complex multiplication.Modular form 5550.2.a.q
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.