Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 16830.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.u1 | 16830ba1 | \([1, -1, 0, -9218484, 10773772240]\) | \(118843307222596927933249/19794099600000000\) | \(14429898608400000000\) | \([2]\) | \(1075200\) | \(2.6841\) | \(\Gamma_0(N)\)-optimal |
16830.u2 | 16830ba2 | \([1, -1, 0, -8318484, 12960592240]\) | \(-87323024620536113533249/48975797371840020000\) | \(-35703356284071374580000\) | \([2]\) | \(2150400\) | \(3.0307\) |
Rank
sage: E.rank()
The elliptic curves in class 16830.u have rank \(0\).
Complex multiplication
The elliptic curves in class 16830.u do not have complex multiplication.Modular form 16830.2.a.u
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.