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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 180336.i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.i1 | 180336bb3 | \([0, -1, 0, -321464, 70258608]\) | \(37159393753/1053\) | \(104107459203072\) | \([2]\) | \(1310720\) | \(1.7914\) | |
| 180336.i2 | 180336bb4 | \([0, -1, 0, -90264, -9422160]\) | \(822656953/85683\) | \(8471262513672192\) | \([2]\) | \(1310720\) | \(1.7914\) | |
| 180336.i3 | 180336bb2 | \([0, -1, 0, -20904, 1009584]\) | \(10218313/1521\) | \(150377441071104\) | \([2, 2]\) | \(655360\) | \(1.4448\) | |
| 180336.i4 | 180336bb1 | \([0, -1, 0, 2216, 84784]\) | \(12167/39\) | \(-3855831822336\) | \([2]\) | \(327680\) | \(1.0982\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 180336.i have rank \(1\).
Complex multiplication
The elliptic curves in class 180336.i do not have complex multiplication.Modular form 180336.2.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 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.
