Show commands:
SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 11858.bo
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11858.bo1 | 11858bl2 | \([1, 1, 1, -2549, -51941]\) | \(-128667913/4096\) | \(-58308726784\) | \([]\) | \(17280\) | \(0.84175\) | |
11858.bo2 | 11858bl1 | \([1, 1, 1, 146, -197]\) | \(24167/16\) | \(-227768464\) | \([]\) | \(5760\) | \(0.29244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11858.bo have rank \(0\).
Complex multiplication
The elliptic curves in class 11858.bo do not have complex multiplication.Modular form 11858.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.