Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 2280.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2280.j1 | 2280j3 | \([0, 1, 0, -480, 3600]\) | \(11968836484/961875\) | \(984960000\) | \([4]\) | \(1024\) | \(0.46886\) | |
2280.j2 | 2280j2 | \([0, 1, 0, -100, -352]\) | \(436334416/81225\) | \(20793600\) | \([2, 2]\) | \(512\) | \(0.12229\) | |
2280.j3 | 2280j1 | \([0, 1, 0, -95, -390]\) | \(5988775936/285\) | \(4560\) | \([2]\) | \(256\) | \(-0.22429\) | \(\Gamma_0(N)\)-optimal |
2280.j4 | 2280j4 | \([0, 1, 0, 200, -1792]\) | \(859687196/1954815\) | \(-2001730560\) | \([2]\) | \(1024\) | \(0.46886\) |
Rank
sage: E.rank()
The elliptic curves in class 2280.j have rank \(0\).
Complex multiplication
The elliptic curves in class 2280.j do not have complex multiplication.Modular form 2280.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.