Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 7600.j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7600.j1 | 7600j2 | \([0, 0, 0, -2575, 50250]\) | \(472058064/475\) | \(1900000000\) | \([2]\) | \(4608\) | \(0.69956\) | |
| 7600.j2 | 7600j1 | \([0, 0, 0, -200, 375]\) | \(3538944/1805\) | \(451250000\) | \([2]\) | \(2304\) | \(0.35298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7600.j have rank \(0\).
Complex multiplication
The elliptic curves in class 7600.j do not have complex multiplication.Modular form 7600.2.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.
