Properties

Label 110946a
Number of curves $4$
Conductor $110946$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 110946a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
110946.i2 110946a1 \([1, 1, 0, -51582360, 142572015936]\) \(3195392484115617625/1508779008\) \(7166857564632572928\) \([2]\) \(9676800\) \(2.9551\) \(\Gamma_0(N)\)-optimal
110946.i3 110946a2 \([1, 1, 0, -51313400, 144132683232]\) \(-3145668549383265625/69470644988448\) \(-329992805384632240807968\) \([2]\) \(19353600\) \(3.3017\)  
110946.i1 110946a3 \([1, 1, 0, -61290135, 85159069653]\) \(5360339745382407625/2442110888312832\) \(11600281287567060617920512\) \([2]\) \(29030400\) \(3.5044\)  
110946.i4 110946a4 \([1, 1, 0, 214124905, 639900043221]\) \(228571521134288888375/169504391772536832\) \(-805163530226852713011904512\) \([2]\) \(58060800\) \(3.8510\)  

Rank

sage: E.rank()
 

The elliptic curves in class 110946a have rank \(1\).

Complex multiplication

The elliptic curves in class 110946a do not have complex multiplication.

Modular form 110946.2.a.a

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