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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 137280i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137280.gk4 | 137280i1 | \([0, 1, 0, 70015, 15419775]\) | \(144794100308831/474439680000\) | \(-124371515473920000\) | \([2]\) | \(1179648\) | \(1.9633\) | \(\Gamma_0(N)\)-optimal |
| 137280.gk3 | 137280i2 | \([0, 1, 0, -667265, 181012863]\) | \(125337052492018849/18404100000000\) | \(4824524390400000000\) | \([2, 2]\) | \(2359296\) | \(2.3099\) | |
| 137280.gk1 | 137280i3 | \([0, 1, 0, -10267265, 12659092863]\) | \(456612868287073618849/12544848030000\) | \(3288556641976320000\) | \([2]\) | \(4718592\) | \(2.6565\) | |
| 137280.gk2 | 137280i4 | \([0, 1, 0, -2863745, -1687313025]\) | \(9908022260084596129/1047363281250000\) | \(274560000000000000000\) | \([2]\) | \(4718592\) | \(2.6565\) |
Rank
sage: E.rank()
The elliptic curves in class 137280i have rank \(0\).
Complex multiplication
The elliptic curves in class 137280i do not have complex multiplication.Modular form 137280.2.a.i
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.
