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Properties

Label 20102.i
Number of curves $3$
Conductor $20102$
CM no
Rank $0$
Graph

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

Elliptic curves in class 20102.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20102.i1 20102b3 \([1, 0, 1, -45241, 29788636]\) \(-69173457625/2550136832\) \(-377511772996763648\) \([]\) \(224532\) \(2.0529\)  
20102.i2 20102b1 \([1, 0, 1, -8211, -287130]\) \(-413493625/152\) \(-22501455128\) \([]\) \(24948\) \(0.95430\) \(\Gamma_0(N)\)-optimal
20102.i3 20102b2 \([1, 0, 1, 5014, -1088036]\) \(94196375/3511808\) \(-519873619277312\) \([]\) \(74844\) \(1.5036\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20102.i have rank \(0\).

Complex multiplication

The elliptic curves in class 20102.i do not have complex multiplication.

Modular form 20102.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} - 2 q^{9} + 6 q^{11} + q^{12} + 5 q^{13} - q^{14} + q^{16} - 3 q^{17} + 2 q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.