Properties

Label 219024.br
Number of curves $4$
Conductor $219024$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 219024.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
219024.br1 219024e3 \([0, 0, 0, -2912715, -1913354118]\) \(-189613868625/128\) \(-1844835128967168\) \([]\) \(2322432\) \(2.2450\)  
219024.br2 219024e4 \([0, 0, 0, -2304315, -2734961814]\) \(-1159088625/2097152\) \(-2448288078992844521472\) \([]\) \(6967296\) \(2.7943\)  
219024.br3 219024e2 \([0, 0, 0, -114075, 15541578]\) \(-140625/8\) \(-9339477840396288\) \([]\) \(995328\) \(1.8213\)  
219024.br4 219024e1 \([0, 0, 0, 7605, 39546]\) \(3375/2\) \(-28825548890112\) \([]\) \(331776\) \(1.2720\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 219024.br have rank \(1\).

Complex multiplication

The elliptic curves in class 219024.br do not have complex multiplication.

Modular form 219024.2.a.br

sage: E.q_eigenform(10)
 
\(q + 2 q^{7} + 3 q^{11} + 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.