Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 152592bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152592.b1 | 152592bi1 | \([0, -1, 0, -476640, -125432064]\) | \(595099203230897/5780865024\) | \(116332092878487552\) | \([2]\) | \(4128768\) | \(2.0942\) | \(\Gamma_0(N)\)-optimal |
152592.b2 | 152592bi2 | \([0, -1, 0, -128480, -305082624]\) | \(-11655394135217/1991891886336\) | \(-40084131174681673728\) | \([2]\) | \(8257536\) | \(2.4408\) |
Rank
sage: E.rank()
The elliptic curves in class 152592bi have rank \(0\).
Complex multiplication
The elliptic curves in class 152592bi do not have complex multiplication.Modular form 152592.2.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 Cremona 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 Cremona labels.