Properties

Label 68400.ds
Number of curves $4$
Conductor $68400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("68400.ds1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 68400.ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
68400.ds1 68400fa4 [0, 0, 0, -2235675, -1284781750] [2] 1179648  
68400.ds2 68400fa2 [0, 0, 0, -183675, -6385750] [2, 2] 589824  
68400.ds3 68400fa1 [0, 0, 0, -111675, 14278250] [2] 294912 \(\Gamma_0(N)\)-optimal
68400.ds4 68400fa3 [0, 0, 0, 716325, -50485750] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 68400.ds have rank \(0\).

Modular form 68400.2.a.ds

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.