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Properties

Label 46410.i
Number of curves $4$
Conductor $46410$
CM no
Rank $0$
Graph

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

Elliptic curves in class 46410.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46410.i1 46410k4 \([1, 1, 0, -381913, -91003007]\) \(6160540455434488353049/107450752500\) \(107450752500\) \([2]\) \(360448\) \(1.6572\)  
46410.i2 46410k3 \([1, 1, 0, -35793, 127737]\) \(5071506329733538969/2926108608384780\) \(2926108608384780\) \([2]\) \(360448\) \(1.6572\)  
46410.i3 46410k2 \([1, 1, 0, -23893, -1426403]\) \(1508565467598193369/6280737699600\) \(6280737699600\) \([2, 2]\) \(180224\) \(1.3107\)  
46410.i4 46410k1 \([1, 1, 0, -773, -43827]\) \(-51184652297689/788010612480\) \(-788010612480\) \([2]\) \(90112\) \(0.96409\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 46410.i have rank \(0\).

Complex multiplication

The elliptic curves in class 46410.i do not have complex multiplication.

Modular form 46410.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.