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SageMath
E = EllipticCurve("im1")
E.isogeny_class()
Elliptic curves in class 81600im
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81600.hj3 | 81600im1 | \([0, 1, 0, -95133, -9290637]\) | \(5951163357184/1129312125\) | \(18068994000000000\) | \([2]\) | \(663552\) | \(1.8370\) | \(\Gamma_0(N)\)-optimal |
| 81600.hj2 | 81600im2 | \([0, 1, 0, -459633, 111358863]\) | \(41948679809104/3291890625\) | \(842724000000000000\) | \([2, 2]\) | \(1327104\) | \(2.1836\) | |
| 81600.hj4 | 81600im3 | \([0, 1, 0, 458367, 501508863]\) | \(10400706415004/112060546875\) | \(-114750000000000000000\) | \([2]\) | \(2654208\) | \(2.5301\) | |
| 81600.hj1 | 81600im4 | \([0, 1, 0, -7209633, 7448608863]\) | \(40472803590982276/281883375\) | \(288648576000000000\) | \([2]\) | \(2654208\) | \(2.5301\) |
Rank
sage: E.rank()
The elliptic curves in class 81600im have rank \(0\).
Complex multiplication
The elliptic curves in class 81600im do not have complex multiplication.Modular form 81600.2.a.im
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.
