Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 271440.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.t1 | 271440t2 | \([0, 0, 0, -2637183, 1648383982]\) | \(10868685473848063696/3741545925\) | \(698262266707200\) | \([2]\) | \(4718592\) | \(2.2044\) | |
271440.t2 | 271440t1 | \([0, 0, 0, -165558, 25515007]\) | \(43025578182363136/787373218125\) | \(9183921216210000\) | \([2]\) | \(2359296\) | \(1.8579\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 271440.t have rank \(2\).
Complex multiplication
The elliptic curves in class 271440.t do not have complex multiplication.Modular form 271440.2.a.t
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.