Properties

Label 265650.dv
Number of curves $4$
Conductor $265650$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dv1")
 
E.isogeny_class()
 

Elliptic curves in class 265650.dv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
265650.dv1 265650dv3 \([1, 0, 1, -239646551, 1427901569498]\) \(97413070452067229637409633/140666577176907936\) \(2197915268389186500000\) \([2]\) \(47185920\) \(3.3658\)  
265650.dv2 265650dv4 \([1, 0, 1, -38390551, -61771758502]\) \(400476194988122984445793/126270124548858769248\) \(1972970696075918269500000\) \([2]\) \(47185920\) \(3.3658\)  
265650.dv3 265650dv2 \([1, 0, 1, -15114551, 21882185498]\) \(24439335640029940889953/902916953746891776\) \(14108077402295184000000\) \([2, 2]\) \(23592960\) \(3.0193\)  
265650.dv4 265650dv1 \([1, 0, 1, 373449, 1221193498]\) \(368637286278891167/41443067603976192\) \(-647547931312128000000\) \([2]\) \(11796480\) \(2.6727\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 265650.dv have rank \(1\).

Complex multiplication

The elliptic curves in class 265650.dv do not have complex multiplication.

Modular form 265650.2.a.dv

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