Properties

Label 13454.d
Number of curves $6$
Conductor $13454$
CM no
Rank $1$
Graph

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

Elliptic curves in class 13454.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13454.d1 13454d6 \([1, 1, 0, -2624030, 1634974964]\) \(2251439055699625/25088\) \(22265692348928\) \([2]\) \(181440\) \(2.1301\)  
13454.d2 13454d5 \([1, 1, 0, -163870, 25538292]\) \(-548347731625/1835008\) \(-1628576354664448\) \([2]\) \(90720\) \(1.7835\)  
13454.d3 13454d4 \([1, 1, 0, -34135, 1975533]\) \(4956477625/941192\) \(835311364527752\) \([2]\) \(60480\) \(1.5808\)  
13454.d4 13454d2 \([1, 1, 0, -10110, -395254]\) \(128787625/98\) \(86975360738\) \([2]\) \(20160\) \(1.0315\)  
13454.d5 13454d1 \([1, 1, 0, -500, -8932]\) \(-15625/28\) \(-24850103068\) \([2]\) \(10080\) \(0.68491\) \(\Gamma_0(N)\)-optimal
13454.d6 13454d3 \([1, 1, 0, 4305, 184229]\) \(9938375/21952\) \(-19482480805312\) \([2]\) \(30240\) \(1.2342\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13454.d have rank \(1\).

Complex multiplication

The elliptic curves in class 13454.d do not have complex multiplication.

Modular form 13454.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} + q^{4} - 2 q^{6} + q^{7} - q^{8} + q^{9} + 2 q^{12} + 4 q^{13} - q^{14} + q^{16} - 6 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.