Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 63536.bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63536.bd1 | 63536t1 | \([0, 1, 0, -157877, 28184099]\) | \(-2258403328/480491\) | \(-92590581381410816\) | \([]\) | \(622080\) | \(1.9769\) | \(\Gamma_0(N)\)-optimal |
63536.bd2 | 63536t2 | \([0, 1, 0, 1112843, -162932189]\) | \(790939860992/517504691\) | \(-99723116993444950016\) | \([]\) | \(1866240\) | \(2.5263\) |
Rank
sage: E.rank()
The elliptic curves in class 63536.bd have rank \(1\).
Complex multiplication
The elliptic curves in class 63536.bd do not have complex multiplication.Modular form 63536.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.