Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 16830u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16830.g2 | 16830u1 | \([1, -1, 0, -7920, -117504]\) | \(75370704203521/35157196800\) | \(25629596467200\) | \([2]\) | \(43008\) | \(1.2673\) | \(\Gamma_0(N)\)-optimal |
16830.g1 | 16830u2 | \([1, -1, 0, -105840, -13219200]\) | \(179865548102096641/119964240000\) | \(87453930960000\) | \([2]\) | \(86016\) | \(1.6139\) |
Rank
sage: E.rank()
The elliptic curves in class 16830u have rank \(1\).
Complex multiplication
The elliptic curves in class 16830u 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 Cremona 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 Cremona labels.