Show commands:
SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 96600.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96600.ci1 | 96600cd1 | \([0, 1, 0, -26387908, 50245846688]\) | \(508017439289666674384/21234429931640625\) | \(84937719726562500000000\) | \([2]\) | \(10321920\) | \(3.1646\) | \(\Gamma_0(N)\)-optimal |
96600.ci2 | 96600cd2 | \([0, 1, 0, 12674592, 186339596688]\) | \(14073614784514581404/945607964406328125\) | \(-15129727430501250000000000\) | \([2]\) | \(20643840\) | \(3.5111\) |
Rank
sage: E.rank()
The elliptic curves in class 96600.ci have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.ci do not have complex multiplication.Modular form 96600.2.a.ci
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.