Properties

Label 289800.bz
Number of curves $4$
Conductor $289800$
CM no
Rank $0$
Graph

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

Elliptic curves in class 289800.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.bz1 289800bz3 \([0, 0, 0, -41733075, 103769252750]\) \(344577854816148242/2716875\) \(63379260000000000\) \([2]\) \(11796480\) \(2.8149\)  
289800.bz2 289800bz2 \([0, 0, 0, -2610075, 1619099750]\) \(168591300897604/472410225\) \(5510192864400000000\) \([2, 2]\) \(5898240\) \(2.4684\)  
289800.bz3 289800bz4 \([0, 0, 0, -1575075, 2915954750]\) \(-18524646126002/146738831715\) \(-3423123466247520000000\) \([2]\) \(11796480\) \(2.8149\)  
289800.bz4 289800bz1 \([0, 0, 0, -229575, 2740250]\) \(458891455696/264449745\) \(771135456420000000\) \([2]\) \(2949120\) \(2.1218\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 289800.bz have rank \(0\).

Complex multiplication

The elliptic curves in class 289800.bz do not have complex multiplication.

Modular form 289800.2.a.bz

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