Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4719.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4719.j1 | 4719c2 | \([1, 1, 0, -1575, -18762]\) | \(244140625/61347\) | \(108679952667\) | \([2]\) | \(3840\) | \(0.82758\) | |
4719.j2 | 4719c1 | \([1, 1, 0, 240, -1701]\) | \(857375/1287\) | \(-2279999007\) | \([2]\) | \(1920\) | \(0.48101\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4719.j have rank \(0\).
Complex multiplication
The elliptic curves in class 4719.j do not have complex multiplication.Modular form 4719.2.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.