Show commands:
SageMath
E = EllipticCurve("fg1")
E.isogeny_class()
Elliptic curves in class 66240fg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
66240.k2 | 66240fg1 | \([0, 0, 0, 2292, 141968]\) | \(27871484/198375\) | \(-9477513216000\) | \([2]\) | \(172032\) | \(1.1716\) | \(\Gamma_0(N)\)-optimal |
66240.k1 | 66240fg2 | \([0, 0, 0, -30828, 1903952]\) | \(33909572018/3234375\) | \(309049344000000\) | \([2]\) | \(344064\) | \(1.5182\) |
Rank
sage: E.rank()
The elliptic curves in class 66240fg have rank \(0\).
Complex multiplication
The elliptic curves in class 66240fg do not have complex multiplication.Modular form 66240.2.a.fg
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.