Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 72075bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72075.bo1 | 72075bo1 | \([0, 1, 1, -8008, 280069]\) | \(-102400/3\) | \(-1664069401875\) | \([]\) | \(182700\) | \(1.1239\) | \(\Gamma_0(N)\)-optimal |
72075.bo2 | 72075bo2 | \([0, 1, 1, 40042, -13606381]\) | \(20480/243\) | \(-84243513469921875\) | \([]\) | \(913500\) | \(1.9286\) |
Rank
sage: E.rank()
The elliptic curves in class 72075bo have rank \(0\).
Complex multiplication
The elliptic curves in class 72075bo do not have complex multiplication.Modular form 72075.2.a.bo
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.