Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 6930r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6930.r1 | 6930r1 | \([1, -1, 1, -263, -1573]\) | \(74246873427/16940\) | \(457380\) | \([2]\) | \(2048\) | \(0.077890\) | \(\Gamma_0(N)\)-optimal |
6930.r2 | 6930r2 | \([1, -1, 1, -233, -1969]\) | \(-51603494067/35870450\) | \(-968502150\) | \([2]\) | \(4096\) | \(0.42446\) |
Rank
sage: E.rank()
The elliptic curves in class 6930r have rank \(0\).
Complex multiplication
The elliptic curves in class 6930r do not have complex multiplication.Modular form 6930.2.a.r
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.