Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 259920d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
259920.d2 | 259920d1 | \([0, 0, 0, -174363, -27998438]\) | \(450714348/475\) | \(617844145996800\) | \([2]\) | \(1843200\) | \(1.7551\) | \(\Gamma_0(N)\)-optimal |
259920.d1 | 259920d2 | \([0, 0, 0, -217683, -13018382]\) | \(438512454/225625\) | \(586951938696960000\) | \([2]\) | \(3686400\) | \(2.1016\) |
Rank
sage: E.rank()
The elliptic curves in class 259920d have rank \(0\).
Complex multiplication
The elliptic curves in class 259920d do not have complex multiplication.Modular form 259920.2.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.