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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 65520.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 65520.cq1 | 65520bg4 | \([0, 0, 0, -107005107, -423599361694]\) | \(181513839777967159549636/1202210966668359375\) | \(897445677774063600000000\) | \([2]\) | \(9830400\) | \(3.4314\) | |
| 65520.cq2 | 65520bg2 | \([0, 0, 0, -10908327, 2743612454]\) | \(769184747004659888464/427705503364400625\) | \(79820111859877902240000\) | \([2, 2]\) | \(4915200\) | \(3.0849\) | |
| 65520.cq3 | 65520bg1 | \([0, 0, 0, -8251122, 9108681311]\) | \(5326172487431504287744/9384070028021325\) | \(109455792806840734800\) | \([2]\) | \(2457600\) | \(2.7383\) | \(\Gamma_0(N)\)-optimal |
| 65520.cq4 | 65520bg3 | \([0, 0, 0, 42673173, 21722179754]\) | \(11512271847440983233884/6935257488834531675\) | \(-5177141974385022557260800\) | \([4]\) | \(9830400\) | \(3.4314\) |
Rank
sage: E.rank()
The elliptic curves in class 65520.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 65520.cq do not have complex multiplication.Modular form 65520.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
