Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 14490.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.d1 | 14490g1 | \([1, -1, 0, -46485, 3866485]\) | \(15238420194810961/12619514880\) | \(9199626347520\) | \([2]\) | \(53760\) | \(1.4159\) | \(\Gamma_0(N)\)-optimal |
14490.d2 | 14490g2 | \([1, -1, 0, -36405, 5582101]\) | \(-7319577278195281/14169067365600\) | \(-10329250109522400\) | \([2]\) | \(107520\) | \(1.7625\) |
Rank
sage: E.rank()
The elliptic curves in class 14490.d have rank \(0\).
Complex multiplication
The elliptic curves in class 14490.d do not have complex multiplication.Modular form 14490.2.a.d
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.