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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 4800.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4800.cq1 | 4800w7 | \([0, 1, 0, -8533633, -9597935137]\) | \(16778985534208729/81000\) | \(331776000000000\) | \([2]\) | \(110592\) | \(2.4086\) | |
| 4800.cq2 | 4800w8 | \([0, 1, 0, -725633, -32623137]\) | \(10316097499609/5859375000\) | \(24000000000000000000\) | \([2]\) | \(110592\) | \(2.4086\) | |
| 4800.cq3 | 4800w6 | \([0, 1, 0, -533633, -149935137]\) | \(4102915888729/9000000\) | \(36864000000000000\) | \([2, 2]\) | \(55296\) | \(2.0620\) | |
| 4800.cq4 | 4800w5 | \([0, 1, 0, -461633, 120568863]\) | \(2656166199049/33750\) | \(138240000000000\) | \([2]\) | \(36864\) | \(1.8593\) | |
| 4800.cq5 | 4800w4 | \([0, 1, 0, -109633, -12071137]\) | \(35578826569/5314410\) | \(21767823360000000\) | \([2]\) | \(36864\) | \(1.8593\) | |
| 4800.cq6 | 4800w2 | \([0, 1, 0, -29633, 1768863]\) | \(702595369/72900\) | \(298598400000000\) | \([2, 2]\) | \(18432\) | \(1.5127\) | |
| 4800.cq7 | 4800w3 | \([0, 1, 0, -21633, -4015137]\) | \(-273359449/1536000\) | \(-6291456000000000\) | \([2]\) | \(27648\) | \(1.7155\) | |
| 4800.cq8 | 4800w1 | \([0, 1, 0, 2367, 136863]\) | \(357911/2160\) | \(-8847360000000\) | \([2]\) | \(9216\) | \(1.1662\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4800.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 4800.cq do not have complex multiplication.Modular form 4800.2.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.
\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
