Properties

Label 348726.b
Number of curves $4$
Conductor $348726$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348726.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.b1 348726b3 \([1, 1, 0, -64564496, 199655028570]\) \(632678989847546725777/80515134\) \(3787905412863054\) \([2]\) \(27648000\) \(2.8492\)  
348726.b2 348726b4 \([1, 1, 0, -4616836, 2160302326]\) \(231331938231569617/90942310746882\) \(4278461129262831693042\) \([2]\) \(27648000\) \(2.8492\)  
348726.b3 348726b2 \([1, 1, 0, -4035626, 3117787680]\) \(154502321244119857/55101928644\) \(2592318777856115364\) \([2, 2]\) \(13824000\) \(2.5026\)  
348726.b4 348726b1 \([1, 1, 0, -216246, 63047556]\) \(-23771111713777/22848457968\) \(-1074925834596029808\) \([2]\) \(6912000\) \(2.1561\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 348726.b have rank \(1\).

Complex multiplication

The elliptic curves in class 348726.b do not have complex multiplication.

Modular form 348726.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.