Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 14490.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.bj1 | 14490bn2 | \([1, -1, 1, -1913, 29531]\) | \(1061520150601/114108750\) | \(83185278750\) | \([2]\) | \(16384\) | \(0.82950\) | |
14490.bj2 | 14490bn1 | \([1, -1, 1, 157, 2207]\) | \(590589719/3332700\) | \(-2429538300\) | \([2]\) | \(8192\) | \(0.48292\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 14490.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.bj do not have complex multiplication.Modular form 14490.2.a.bj
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.