Properties

Label 101400.do
Number of curves $4$
Conductor $101400$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("do1")
 
E.isogeny_class()
 

Elliptic curves in class 101400.do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101400.do1 101400di4 \([0, 1, 0, -35153408, 80211350688]\) \(31103978031362/195\) \(30119288160000000\) \([2]\) \(6193152\) \(2.7676\)  
101400.do2 101400di3 \([0, 1, 0, -3043408, 199990688]\) \(20183398562/11567205\) \(1786646054363040000000\) \([2]\) \(6193152\) \(2.7676\)  
101400.do3 101400di2 \([0, 1, 0, -2198408, 1251170688]\) \(15214885924/38025\) \(2936630595600000000\) \([2, 2]\) \(3096576\) \(2.4210\)  
101400.do4 101400di1 \([0, 1, 0, -85908, 34370688]\) \(-3631696/24375\) \(-470613877500000000\) \([2]\) \(1548288\) \(2.0744\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 101400.do have rank \(1\).

Complex multiplication

The elliptic curves in class 101400.do do not have complex multiplication.

Modular form 101400.2.a.do

sage: E.q_eigenform(10)
 
\(q + q^{3} + 4 q^{7} + q^{9} - 4 q^{11} - 6 q^{17} + O(q^{20})\) 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.