Properties

Label 215600.hf
Number of curves 4
Conductor 215600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("215600.hf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 215600.hf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
215600.hf1 215600es4 [0, -1, 0, -511874008, -4331034889488] [2] 95551488  
215600.hf2 215600es2 [0, -1, 0, -70090008, 223873398512] [2] 31850496  
215600.hf3 215600es1 [0, -1, 0, -1098008, 8618358512] [2] 15925248 \(\Gamma_0(N)\)-optimal
215600.hf4 215600es3 [0, -1, 0, 9877992, -232151177488] [2] 47775744  

Rank

sage: E.rank()
 

The elliptic curves in class 215600.hf have rank \(0\).

Modular form 215600.2.a.hf

sage: E.q_eigenform(10)
 
\( q + 2q^{3} + q^{9} + q^{11} - 4q^{13} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.