Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 1152.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1152.j1 | 1152q1 | \([0, 0, 0, -30, -52]\) | \(16000/3\) | \(559872\) | \([2]\) | \(128\) | \(-0.17914\) | \(\Gamma_0(N)\)-optimal |
| 1152.j2 | 1152q2 | \([0, 0, 0, 60, -304]\) | \(4000/9\) | \(-53747712\) | \([2]\) | \(256\) | \(0.16743\) |
Rank
sage: E.rank()
The elliptic curves in class 1152.j have rank \(1\).
Complex multiplication
The elliptic curves in class 1152.j do not have complex multiplication.Modular form 1152.2.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.
