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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 154560.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.cq1 | 154560gy3 | \([0, -1, 0, -27697985, 56116663617]\) | \(8964546681033941529169/31696875000\) | \(8309145600000000\) | \([4]\) | \(7077888\) | \(2.6970\) | |
| 154560.cq2 | 154560gy4 | \([0, -1, 0, -2307905, 243861825]\) | \(5186062692284555089/2903809817953800\) | \(761216320917680947200\) | \([2]\) | \(7077888\) | \(2.6970\) | |
| 154560.cq3 | 154560gy2 | \([0, -1, 0, -1731905, 876425025]\) | \(2191574502231419089/4115217960000\) | \(1078779696906240000\) | \([2, 2]\) | \(3538944\) | \(2.3504\) | |
| 154560.cq4 | 154560gy1 | \([0, -1, 0, -73025, 22765377]\) | \(-164287467238609/757170892800\) | \(-198487806522163200\) | \([2]\) | \(1769472\) | \(2.0039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 154560.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 154560.cq do not have complex multiplication.Modular form 154560.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
