Show commands:
SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 5880.bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5880.bi1 | 5880q2 | \([0, 1, 0, -100, -400]\) | \(1272112/75\) | \(6585600\) | \([2]\) | \(1536\) | \(0.061602\) | |
5880.bi2 | 5880q1 | \([0, 1, 0, 5, -22]\) | \(2048/45\) | \(-246960\) | \([2]\) | \(768\) | \(-0.28497\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5880.bi have rank \(0\).
Complex multiplication
The elliptic curves in class 5880.bi do not have complex multiplication.Modular form 5880.2.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.