Show commands:
SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 43560.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 43560.by1 | 43560cc2 | \([0, 0, 0, -8620887, 9742619194]\) | \(161019290864/135\) | \(59406700034499840\) | \([2]\) | \(1216512\) | \(2.5214\) | |
| 43560.by2 | 43560cc1 | \([0, 0, 0, -535062, 154447909]\) | \(-615962624/18225\) | \(-501244031541092400\) | \([2]\) | \(608256\) | \(2.1749\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 43560.by have rank \(0\).
Complex multiplication
The elliptic curves in class 43560.by do not have complex multiplication.Modular form 43560.2.a.by
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.
