Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 110352.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110352.j1 | 110352y4 | \([0, -1, 0, -196544, 33603264]\) | \(115714886617/1539\) | \(11167467024384\) | \([2]\) | \(552960\) | \(1.6471\) | |
110352.j2 | 110352y2 | \([0, -1, 0, -12624, 497664]\) | \(30664297/3249\) | \(23575763718144\) | \([2, 2]\) | \(276480\) | \(1.3005\) | |
110352.j3 | 110352y1 | \([0, -1, 0, -2944, -52160]\) | \(389017/57\) | \(413609889792\) | \([2]\) | \(138240\) | \(0.95394\) | \(\Gamma_0(N)\)-optimal |
110352.j4 | 110352y3 | \([0, -1, 0, 16416, 2425920]\) | \(67419143/390963\) | \(-2836950234083328\) | \([2]\) | \(552960\) | \(1.6471\) |
Rank
sage: E.rank()
The elliptic curves in class 110352.j have rank \(1\).
Complex multiplication
The elliptic curves in class 110352.j do not have complex multiplication.Modular form 110352.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.