Show commands:
SageMath
E = EllipticCurve("km1")
E.isogeny_class()
Elliptic curves in class 277200km
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.km2 | 277200km1 | \([0, 0, 0, -4800, -7418000]\) | \(-262144/509355\) | \(-23764466880000000\) | \([]\) | \(1990656\) | \(1.8212\) | \(\Gamma_0(N)\)-optimal |
277200.km1 | 277200km2 | \([0, 0, 0, -3028800, -2028962000]\) | \(-65860951343104/3493875\) | \(-163010232000000000\) | \([]\) | \(5971968\) | \(2.3705\) |
Rank
sage: E.rank()
The elliptic curves in class 277200km have rank \(0\).
Complex multiplication
The elliptic curves in class 277200km do not have complex multiplication.Modular form 277200.2.a.km
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.