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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 117600cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 117600.gb3 | 117600cq1 | \([0, 1, 0, -37158, 2642688]\) | \(48228544/2025\) | \(238239225000000\) | \([2, 2]\) | \(442368\) | \(1.5234\) | \(\Gamma_0(N)\)-optimal |
| 117600.gb4 | 117600cq2 | \([0, 1, 0, 17967, 9864063]\) | \(85184/5625\) | \(-42353640000000000\) | \([2]\) | \(884736\) | \(1.8700\) | |
| 117600.gb2 | 117600cq3 | \([0, 1, 0, -98408, -8382312]\) | \(111980168/32805\) | \(30875803560000000\) | \([2]\) | \(884736\) | \(1.8700\) | |
| 117600.gb1 | 117600cq4 | \([0, 1, 0, -588408, 173530188]\) | \(23937672968/45\) | \(42353640000000\) | \([2]\) | \(884736\) | \(1.8700\) |
Rank
sage: E.rank()
The elliptic curves in class 117600cq have rank \(1\).
Complex multiplication
The elliptic curves in class 117600cq do not have complex multiplication.Modular form 117600.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
