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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 7326.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7326.k1 | 7326i3 | \([1, -1, 1, -50466839, -137980449489]\) | \(19499096390516434897995817/15393430272\) | \(11221810668288\) | \([2]\) | \(491520\) | \(2.7086\) | |
| 7326.k2 | 7326i2 | \([1, -1, 1, -3154199, -2155322577]\) | \(4760617885089919932457/133756441657344\) | \(97508445968203776\) | \([2, 2]\) | \(245760\) | \(2.3620\) | |
| 7326.k3 | 7326i4 | \([1, -1, 1, -3027479, -2336532177]\) | \(-4209586785160189454377/801182513521564416\) | \(-584062052357220459264\) | \([2]\) | \(491520\) | \(2.7086\) | |
| 7326.k4 | 7326i1 | \([1, -1, 1, -205079, -30776529]\) | \(1308451928740468777/194033737531392\) | \(141450594660384768\) | \([4]\) | \(122880\) | \(2.0155\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7326.k have rank \(0\).
Complex multiplication
The elliptic curves in class 7326.k do not have complex multiplication.Modular form 7326.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
