Show commands:
SageMath
E = EllipticCurve("bv1")
E.isogeny_class()
Elliptic curves in class 117600.bv
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117600.bv1 | 117600bl1 | \([0, -1, 0, -26378, -1640148]\) | \(2156689088/81\) | \(76236552000\) | \([2]\) | \(221184\) | \(1.1745\) | \(\Gamma_0(N)\)-optimal |
117600.bv2 | 117600bl2 | \([0, -1, 0, -25153, -1800623]\) | \(-29218112/6561\) | \(-395210285568000\) | \([2]\) | \(442368\) | \(1.5210\) |
Rank
sage: E.rank()
The elliptic curves in class 117600.bv have rank \(1\).
Complex multiplication
The elliptic curves in class 117600.bv do not have complex multiplication.Modular form 117600.2.a.bv
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.