Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("68400.fv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 68400fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
68400.fv4 68400fs1 [0, 0, 0, -36075, 4500250] [2] 442368 \(\Gamma_0(N)\)-optimal
68400.fv3 68400fs2 [0, 0, 0, -684075, 217692250] [2, 2] 884736  
68400.fv2 68400fs3 [0, 0, 0, -792075, 144360250] [2] 1769472  
68400.fv1 68400fs4 [0, 0, 0, -10944075, 13935312250] [2] 1769472  

Rank

sage: E.rank()
 

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

Modular form 68400.2.a.fv

sage: E.q_eigenform(10)
 
\( q + 4q^{7} - 4q^{11} + 2q^{13} - 2q^{17} + q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.