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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 88725v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88725.o3 | 88725v1 | \([1, 1, 1, -4313813, -3416736094]\) | \(117713838907729/1322517105\) | \(99742772891686640625\) | \([2]\) | \(3483648\) | \(2.6512\) | \(\Gamma_0(N)\)-optimal |
| 88725.o2 | 88725v2 | \([1, 1, 1, -7883938, 3052330406]\) | \(718576775407009/362361861225\) | \(27328929578399703515625\) | \([2, 2]\) | \(6967296\) | \(2.9978\) | |
| 88725.o4 | 88725v3 | \([1, 1, 1, 29190437, 23591534156]\) | \(36472485598112591/24291459037755\) | \(-1832034892290112090546875\) | \([2]\) | \(13934592\) | \(3.3444\) | |
| 88725.o1 | 88725v4 | \([1, 1, 1, -102080313, 396604785156]\) | \(1559802282754777489/1481059636875\) | \(111699874762577841796875\) | \([2]\) | \(13934592\) | \(3.3444\) |
Rank
sage: E.rank()
The elliptic curves in class 88725v have rank \(0\).
Complex multiplication
The elliptic curves in class 88725v do not have complex multiplication.Modular form 88725.2.a.v
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.
