Show commands:
SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 271440.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
271440.ba1 | 271440ba2 | \([0, 0, 0, -5763, 167762]\) | \(28355811844/122525\) | \(91464422400\) | \([2]\) | \(221184\) | \(0.95663\) | |
271440.ba2 | 271440ba1 | \([0, 0, 0, -543, -322]\) | \(94875856/54665\) | \(10201800960\) | \([2]\) | \(110592\) | \(0.61005\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 271440.ba have rank \(2\).
Complex multiplication
The elliptic curves in class 271440.ba do not have complex multiplication.Modular form 271440.2.a.ba
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.