Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 35280.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
35280.bw1 | 35280cy2 | \([0, 0, 0, -24003, 1024002]\) | \(55306341/15625\) | \(432081216000000\) | \([2]\) | \(147456\) | \(1.5152\) | |
35280.bw2 | 35280cy1 | \([0, 0, 0, -8883, -309582]\) | \(2803221/125\) | \(3456649728000\) | \([2]\) | \(73728\) | \(1.1686\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 35280.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.bw do not have complex multiplication.Modular form 35280.2.a.bw
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 LMFDB 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 LMFDB labels.