Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 14490d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14490.o1 | 14490d1 | \([1, -1, 0, -1365, -16219]\) | \(14295828483/2254000\) | \(44365482000\) | \([2]\) | \(13824\) | \(0.76579\) | \(\Gamma_0(N)\)-optimal |
14490.o2 | 14490d2 | \([1, -1, 0, 2415, -92575]\) | \(79119341757/231437500\) | \(-4555384312500\) | \([2]\) | \(27648\) | \(1.1124\) |
Rank
sage: E.rank()
The elliptic curves in class 14490d have rank \(0\).
Complex multiplication
The elliptic curves in class 14490d 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 Cremona 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 Cremona labels.