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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 82800.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82800.i1 | 82800es3 | \([0, 0, 0, -2737200, -1743042125]\) | \(12444451776495616/912525\) | \(166307681250000\) | \([2]\) | \(1161216\) | \(2.1795\) | |
82800.i2 | 82800es4 | \([0, 0, 0, -2731575, -1750562750]\) | \(-772993034343376/6661615005\) | \(-19425269354580000000\) | \([2]\) | \(2322432\) | \(2.5260\) | |
82800.i3 | 82800es1 | \([0, 0, 0, -37200, -1879625]\) | \(31238127616/9703125\) | \(1768394531250000\) | \([2]\) | \(387072\) | \(1.6302\) | \(\Gamma_0(N)\)-optimal |
82800.i4 | 82800es2 | \([0, 0, 0, 103425, -12707750]\) | \(41957807024/48205125\) | \(-140566144500000000\) | \([2]\) | \(774144\) | \(1.9767\) |
Rank
sage: E.rank()
The elliptic curves in class 82800.i have rank \(0\).
Complex multiplication
The elliptic curves in class 82800.i do not have complex multiplication.Modular form 82800.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.