Properties

Label 14400dp
Number of curves 8
Conductor 14400
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("14400.cz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.cz7 14400dp1 [0, 0, 0, -300, 322000] [2] 24576 \(\Gamma_0(N)\)-optimal
14400.cz6 14400dp2 [0, 0, 0, -72300, 7378000] [2, 2] 49152  
14400.cz5 14400dp3 [0, 0, 0, -144300, -9758000] [2, 2] 98304  
14400.cz4 14400dp4 [0, 0, 0, -1152300, 476098000] [2] 98304  
14400.cz2 14400dp5 [0, 0, 0, -1944300, -1042958000] [2, 2] 196608  
14400.cz8 14400dp6 [0, 0, 0, 503700, -73262000] [2] 196608  
14400.cz1 14400dp7 [0, 0, 0, -31104300, -66769598000] [2] 393216  
14400.cz3 14400dp8 [0, 0, 0, -1584300, -1441118000] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 14400dp have rank \(1\).

Modular form 14400.2.a.cz

sage: E.q_eigenform(10)
 
\( q + 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.