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SageMath
E = EllipticCurve("cr1")
E.isogeny_class()
Elliptic curves in class 154560.cr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.cr1 | 154560gz1 | \([0, -1, 0, -18394145, 19095172257]\) | \(2625564132023811051529/918925030195200000\) | \(240890683115490508800000\) | \([2]\) | \(13824000\) | \(3.1880\) | \(\Gamma_0(N)\)-optimal |
| 154560.cr2 | 154560gz2 | \([0, -1, 0, 55006175, 133408830625]\) | \(70213095586874240921591/69970703040000000000\) | \(-18342399977717760000000000\) | \([2]\) | \(27648000\) | \(3.5345\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.cr have rank \(0\).
Complex multiplication
The elliptic curves in class 154560.cr do not have complex multiplication.Modular form 154560.2.a.cr
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
