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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 76440cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76440.ce4 | 76440cq1 | \([0, 1, 0, -996, -43296]\) | \(-3631696/24375\) | \(-734129760000\) | \([2]\) | \(110592\) | \(0.96019\) | \(\Gamma_0(N)\)-optimal |
| 76440.ce3 | 76440cq2 | \([0, 1, 0, -25496, -1572096]\) | \(15214885924/38025\) | \(4580969702400\) | \([2, 2]\) | \(221184\) | \(1.3068\) | |
| 76440.ce2 | 76440cq3 | \([0, 1, 0, -35296, -262816]\) | \(20183398562/11567205\) | \(2787061966940160\) | \([2]\) | \(442368\) | \(1.6533\) | |
| 76440.ce1 | 76440cq4 | \([0, 1, 0, -407696, -100332576]\) | \(31103978031362/195\) | \(46984304640\) | \([2]\) | \(442368\) | \(1.6533\) |
Rank
sage: E.rank()
The elliptic curves in class 76440cq have rank \(0\).
Complex multiplication
The elliptic curves in class 76440cq do not have complex multiplication.Modular form 76440.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
