Properties

Label 82800.i
Number of curves $4$
Conductor $82800$
CM no
Rank $0$
Graph

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Show commands: 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)
 
\(q - 4 q^{7} - 2 q^{13} + 6 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.