Show commands:
SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 111090.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111090.cq1 | 111090cq4 | \([1, 0, 0, -255168451, 1535392465481]\) | \(12411881707829361287041/303132494474220600\) | \(44874488304278834103113400\) | \([2]\) | \(65691648\) | \(3.7062\) | |
111090.cq2 | 111090cq2 | \([1, 0, 0, -31401451, -66911610319]\) | \(23131609187144855041/322060536000000\) | \(47676517758576504000000\) | \([2]\) | \(21897216\) | \(3.1569\) | |
111090.cq3 | 111090cq1 | \([1, 0, 0, -253931, -2803784655]\) | \(-12232183057921/22933241856000\) | \(-3394942845804969984000\) | \([2]\) | \(10948608\) | \(2.8104\) | \(\Gamma_0(N)\)-optimal |
111090.cq4 | 111090cq3 | \([1, 0, 0, 2285269, 75681363825]\) | \(8915971454369279/16719623332762560\) | \(-2475104303810648395515840\) | \([2]\) | \(32845824\) | \(3.3597\) |
Rank
sage: E.rank()
The elliptic curves in class 111090.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 111090.cq do not have complex multiplication.Modular form 111090.2.a.cq
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.