Properties

Label 9408.d
Number of curves 2
Conductor 9408
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("9408.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.d1 9408d2 [0, -1, 0, -45537, -3744159] [] 34560  
9408.d2 9408d1 [0, -1, 0, 1503, -27999] [] 11520 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9408.d have rank \(1\).

Modular form 9408.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{3} - 3q^{5} + q^{9} - 3q^{11} + 4q^{13} + 3q^{15} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.