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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 129360.ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129360.ct1 | 129360bj4 | \([0, -1, 0, -1459040, 678717600]\) | \(1425631925916578/270703125\) | \(65224605600000000\) | \([4]\) | \(1572864\) | \(2.2275\) | |
| 129360.ct2 | 129360bj3 | \([0, -1, 0, -639760, -190512608]\) | \(120186986927618/4332064275\) | \(1043789885213644800\) | \([2]\) | \(1572864\) | \(2.2275\) | |
| 129360.ct3 | 129360bj2 | \([0, -1, 0, -100760, 8270592]\) | \(939083699236/300155625\) | \(36160521344640000\) | \([2, 2]\) | \(786432\) | \(1.8809\) | |
| 129360.ct4 | 129360bj1 | \([0, -1, 0, 17820, 871200]\) | \(20777545136/23059575\) | \(-694511600428800\) | \([2]\) | \(393216\) | \(1.5344\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129360.ct have rank \(1\).
Complex multiplication
The elliptic curves in class 129360.ct do not have complex multiplication.Modular form 129360.2.a.ct
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.
