Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 142956bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
142956.u2 | 142956bd1 | \([0, 0, 0, -86640, -28951839]\) | \(-3538944000/15768841\) | \(-320483095427773872\) | \([2]\) | \(1036800\) | \(2.0439\) | \(\Gamma_0(N)\)-optimal |
142956.u1 | 142956bd2 | \([0, 0, 0, -2041455, -1120911498]\) | \(2893462182000/5285401\) | \(1718712666892438272\) | \([2]\) | \(2073600\) | \(2.3905\) |
Rank
sage: E.rank()
The elliptic curves in class 142956bd have rank \(0\).
Complex multiplication
The elliptic curves in class 142956bd do not have complex multiplication.Modular form 142956.2.a.bd
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.