Properties

Label 308550.bz
Number of curves $4$
Conductor $308550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 308550.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.bz1 308550bz4 \([1, 1, 0, -666599650, 6573377207500]\) \(1183430669265454849849/10449720703125000\) \(289254963414825439453125000\) \([2]\) \(199065600\) \(3.9009\)  
308550.bz2 308550bz3 \([1, 1, 0, -72126650, -67480675500]\) \(1499114720492202169/796539777000000\) \(22048731310654640625000000\) \([2]\) \(99532800\) \(3.5544\)  
308550.bz3 308550bz2 \([1, 1, 0, -57168025, -161023431125]\) \(746461053445307689/27443694341250\) \(759659040482487363281250\) \([2]\) \(66355200\) \(3.3516\)  
308550.bz4 308550bz1 \([1, 1, 0, -56653775, -164154699375]\) \(726497538898787209/1038579300\) \(28748540363864062500\) \([2]\) \(33177600\) \(3.0050\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308550.bz have rank \(0\).

Complex multiplication

The elliptic curves in class 308550.bz do not have complex multiplication.

Modular form 308550.2.a.bz

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} - q^{8} + q^{9} - q^{12} - 4 q^{13} - 2 q^{14} + q^{16} - q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content 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 LMFDB 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 LMFDB labels.