Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 4560.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4560.q1 | 4560t4 | \([0, -1, 0, -15480, 746352]\) | \(100162392144121/23457780\) | \(96083066880\) | \([4]\) | \(12288\) | \(1.0978\) | |
4560.q2 | 4560t3 | \([0, -1, 0, -7160, -224400]\) | \(9912050027641/311647500\) | \(1276508160000\) | \([2]\) | \(12288\) | \(1.0978\) | |
4560.q3 | 4560t2 | \([0, -1, 0, -1080, 9072]\) | \(34043726521/11696400\) | \(47908454400\) | \([2, 2]\) | \(6144\) | \(0.75126\) | |
4560.q4 | 4560t1 | \([0, -1, 0, 200, 880]\) | \(214921799/218880\) | \(-896532480\) | \([2]\) | \(3072\) | \(0.40469\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.q have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.q do not have complex multiplication.Modular form 4560.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.