Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 130536.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
130536.bi1 | 130536k1 | \([0, 0, 0, -4410, 83349]\) | \(6912000/1813\) | \(2487903637968\) | \([2]\) | \(172032\) | \(1.0873\) | \(\Gamma_0(N)\)-optimal |
130536.bi2 | 130536k2 | \([0, 0, 0, 11025, 537138]\) | \(6750000/9583\) | \(-210405564811008\) | \([2]\) | \(344064\) | \(1.4339\) |
Rank
sage: E.rank()
The elliptic curves in class 130536.bi have rank \(2\).
Complex multiplication
The elliptic curves in class 130536.bi do not have complex multiplication.Modular form 130536.2.a.bi
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.