Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 443760.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
443760.bo1 | 443760bo2 | \([0, -1, 0, -16961572840, 850256937331312]\) | \(262147686417280027/22500\) | \(46318935116099450880000\) | \([2]\) | \(348733440\) | \(4.2354\) | \(\Gamma_0(N)\)-optimal* |
443760.bo2 | 443760bo1 | \([0, -1, 0, -1060172840, 13283568051312]\) | \(64014401080027/18750000\) | \(38599112596749542400000000\) | \([2]\) | \(174366720\) | \(3.8888\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 443760.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 443760.bo do not have complex multiplication.Modular form 443760.2.a.bo
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.