Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 2873.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2873.b1 | 2873b2 | \([1, -1, 0, -1980289, 1073103084]\) | \(177930109857804849/634933\) | \(3064700318797\) | \([2]\) | \(40320\) | \(2.0376\) | |
2873.b2 | 2873b1 | \([1, -1, 0, -123824, 16774499]\) | \(43499078731809/82055753\) | \(396067447082177\) | \([2]\) | \(20160\) | \(1.6911\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2873.b have rank \(0\).
Complex multiplication
The elliptic curves in class 2873.b do not have complex multiplication.Modular form 2873.2.a.b
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.