Properties

Label 95304.d
Number of curves 4
Conductor 95304
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("95304.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 95304.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95304.d1 95304n4 [0, -1, 0, -254264, -49263972] [2] 580608  
95304.d2 95304n3 [0, -1, 0, -37664, 1749660] [2] 580608  
95304.d3 95304n2 [0, -1, 0, -16004, -754236] [2, 2] 290304  
95304.d4 95304n1 [0, -1, 0, 241, -39456] [2] 145152 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 95304.d have rank \(1\).

Modular form 95304.2.a.d

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

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.