Properties

Label 20808.i
Number of curves $6$
Conductor $20808$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20808.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20808.i1 20808l5 \([0, 0, 0, -999651, 384697726]\) \(3065617154/9\) \(324334776748032\) \([2]\) \(163840\) \(2.0137\)  
20808.i2 20808l3 \([0, 0, 0, -167331, -26343506]\) \(28756228/3\) \(54055796124672\) \([2]\) \(81920\) \(1.6671\)  
20808.i3 20808l4 \([0, 0, 0, -63291, 5846470]\) \(1556068/81\) \(1459506495366144\) \([2, 2]\) \(81920\) \(1.6671\)  
20808.i4 20808l2 \([0, 0, 0, -11271, -343910]\) \(35152/9\) \(40541847093504\) \([2, 2]\) \(40960\) \(1.3206\)  
20808.i5 20808l1 \([0, 0, 0, 1734, -34391]\) \(2048/3\) \(-844621814448\) \([2]\) \(20480\) \(0.97399\) \(\Gamma_0(N)\)-optimal
20808.i6 20808l6 \([0, 0, 0, 40749, 23179534]\) \(207646/6561\) \(-236440052249315328\) \([2]\) \(163840\) \(2.0137\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20808.i have rank \(0\).

Complex multiplication

The elliptic curves in class 20808.i do not have complex multiplication.

Modular form 20808.2.a.i

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + 4q^{11} - 2q^{13} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.