Properties

Label 215600er
Number of curves $4$
Conductor $215600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("er1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 215600er

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
215600.he4 215600er1 \([0, -1, 0, -55533, 4952312]\) \(643956736/15125\) \(444860281250000\) \([2]\) \(995328\) \(1.5962\) \(\Gamma_0(N)\)-optimal
215600.he3 215600er2 \([0, -1, 0, -122908, -9331188]\) \(436334416/171875\) \(80883687500000000\) \([2]\) \(1990656\) \(1.9428\)  
215600.he2 215600er3 \([0, -1, 0, -545533, -152950188]\) \(610462990336/8857805\) \(260527975111250000\) \([2]\) \(2985984\) \(2.1455\)  
215600.he1 215600er4 \([0, -1, 0, -8697908, -9870581188]\) \(154639330142416/33275\) \(15659081900000000\) \([2]\) \(5971968\) \(2.4921\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 215600er do not have complex multiplication.

Modular form 215600.2.a.er

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.