Show commands:
SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 270504bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270504.bx2 | 270504bx1 | \([0, 0, 0, 32946, -564995]\) | \(14047232/8619\) | \(-2426598472909104\) | \([2]\) | \(1179648\) | \(1.6413\) | \(\Gamma_0(N)\)-optimal |
270504.bx1 | 270504bx2 | \([0, 0, 0, -136119, -4588742]\) | \(61918288/33813\) | \(152315719530294528\) | \([2]\) | \(2359296\) | \(1.9878\) |
Rank
sage: E.rank()
The elliptic curves in class 270504bx have rank \(0\).
Complex multiplication
The elliptic curves in class 270504bx do not have complex multiplication.Modular form 270504.2.a.bx
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.