Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 11088.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11088.j1 | 11088bb1 | \([0, 0, 0, -411, -1206]\) | \(69426531/34496\) | \(3814981632\) | \([2]\) | \(4608\) | \(0.53148\) | \(\Gamma_0(N)\)-optimal |
11088.j2 | 11088bb2 | \([0, 0, 0, 1509, -9270]\) | \(3436115229/2324168\) | \(-257034387456\) | \([2]\) | \(9216\) | \(0.87806\) |
Rank
sage: E.rank()
The elliptic curves in class 11088.j have rank \(1\).
Complex multiplication
The elliptic curves in class 11088.j do not have complex multiplication.Modular form 11088.2.a.j
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.