Show commands:
SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 96600.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
96600.ce1 | 96600ct2 | \([0, 1, 0, -1832208, 953957088]\) | \(170054560416634/1633023\) | \(6532092000000000\) | \([2]\) | \(1259520\) | \(2.1963\) | |
96600.ce2 | 96600ct1 | \([0, 1, 0, -117208, 14137088]\) | \(89036727188/8117781\) | \(16235562000000000\) | \([2]\) | \(629760\) | \(1.8497\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96600.ce have rank \(0\).
Complex multiplication
The elliptic curves in class 96600.ce do not have complex multiplication.Modular form 96600.2.a.ce
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.