Show commands:
SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 43560.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
43560.bj1 | 43560cp4 | \([0, 0, 0, -1760187, -853817866]\) | \(228027144098/12890625\) | \(34094754381600000000\) | \([2]\) | \(1474560\) | \(2.5026\) | |
43560.bj2 | 43560cp2 | \([0, 0, 0, -322707, 53807006]\) | \(2810381476/680625\) | \(900101515674240000\) | \([2, 2]\) | \(737280\) | \(2.1560\) | |
43560.bj3 | 43560cp1 | \([0, 0, 0, -300927, 63533954]\) | \(9115564624/825\) | \(272758035052800\) | \([4]\) | \(368640\) | \(1.8095\) | \(\Gamma_0(N)\)-optimal |
43560.bj4 | 43560cp3 | \([0, 0, 0, 766293, 338907206]\) | \(18814587262/29648025\) | \(-78416844045539788800\) | \([2]\) | \(1474560\) | \(2.5026\) |
Rank
sage: E.rank()
The elliptic curves in class 43560.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 43560.bj do not have complex multiplication.Modular form 43560.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.