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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 27600cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 27600.dg4 | 27600cq1 | \([0, 1, 0, 182592, -18844812]\) | \(10519294081031/8500170375\) | \(-544010904000000000\) | \([2]\) | \(460800\) | \(2.0910\) | \(\Gamma_0(N)\)-optimal |
| 27600.dg3 | 27600cq2 | \([0, 1, 0, -875408, -164848812]\) | \(1159246431432649/488076890625\) | \(31236921000000000000\) | \([2, 2]\) | \(921600\) | \(2.4376\) | |
| 27600.dg2 | 27600cq3 | \([0, 1, 0, -6625408, 6447651188]\) | \(502552788401502649/10024505152875\) | \(641568329784000000000\) | \([4]\) | \(1843200\) | \(2.7841\) | |
| 27600.dg1 | 27600cq4 | \([0, 1, 0, -12053408, -16104676812]\) | \(3026030815665395929/1364501953125\) | \(87328125000000000000\) | \([2]\) | \(1843200\) | \(2.7841\) |
Rank
sage: E.rank()
The elliptic curves in class 27600cq have rank \(1\).
Complex multiplication
The elliptic curves in class 27600cq do not have complex multiplication.Modular form 27600.2.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.
