Show commands:
SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 124950fk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124950.ft2 | 124950fk1 | \([1, 1, 1, 620437, 150925781]\) | \(41890384817/39795300\) | \(-25091935885110937500\) | \([2]\) | \(3096576\) | \(2.4096\) | \(\Gamma_0(N)\)-optimal |
124950.ft1 | 124950fk2 | \([1, 1, 1, -3238313, 1362573281]\) | \(5956317014383/2172381210\) | \(1369740900039444843750\) | \([2]\) | \(6193152\) | \(2.7561\) |
Rank
sage: E.rank()
The elliptic curves in class 124950fk have rank \(0\).
Complex multiplication
The elliptic curves in class 124950fk do not have complex multiplication.Modular form 124950.2.a.fk
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.