Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 206856.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 206856.bd1 | 206856m2 | \([0, 0, 0, -73515, -7351162]\) | \(6097250/289\) | \(2082645907310592\) | \([2]\) | \(737280\) | \(1.6999\) | |
| 206856.bd2 | 206856m1 | \([0, 0, 0, -12675, 399854]\) | \(62500/17\) | \(61254291391488\) | \([2]\) | \(368640\) | \(1.3534\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 206856.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 206856.bd do not have complex multiplication.Modular form 206856.2.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 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.
