Show commands:
SageMath
E = EllipticCurve("ea1")
E.isogeny_class()
Elliptic curves in class 352800ea
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
352800.ea2 | 352800ea1 | \([0, 0, 0, 18375, -5316500]\) | \(8000/147\) | \(-12607619787000000\) | \([2]\) | \(1769472\) | \(1.7699\) | \(\Gamma_0(N)\)-optimal |
352800.ea1 | 352800ea2 | \([0, 0, 0, -367500, -80948000]\) | \(1000000/63\) | \(345808999872000000\) | \([2]\) | \(3538944\) | \(2.1164\) |
Rank
sage: E.rank()
The elliptic curves in class 352800ea have rank \(0\).
Complex multiplication
The elliptic curves in class 352800ea do not have complex multiplication.Modular form 352800.2.a.ea
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.