Show commands:
SageMath
E = EllipticCurve("cv1")
E.isogeny_class()
Elliptic curves in class 14400cv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
14400.ee2 | 14400cv1 | \([0, 0, 0, -300, 18000]\) | \(-108/5\) | \(-138240000000\) | \([2]\) | \(12288\) | \(0.81771\) | \(\Gamma_0(N)\)-optimal |
14400.ee1 | 14400cv2 | \([0, 0, 0, -12300, 522000]\) | \(3721734/25\) | \(1382400000000\) | \([2]\) | \(24576\) | \(1.1643\) |
Rank
sage: E.rank()
The elliptic curves in class 14400cv have rank \(0\).
Complex multiplication
The elliptic curves in class 14400cv do not have complex multiplication.Modular form 14400.2.a.cv
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.