Properties

Label 147030bf
Number of curves $4$
Conductor $147030$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 147030bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
147030.bo3 147030bf1 \([1, 1, 1, -299556, 62978469]\) \(615882348586441/21715200\) \(104815122796800\) \([4]\) \(2064384\) \(1.7801\) \(\Gamma_0(N)\)-optimal
147030.bo2 147030bf2 \([1, 1, 1, -313076, 56964773]\) \(703093388853961/115124490000\) \(555683924452410000\) \([2, 2]\) \(4128768\) \(2.1266\)  
147030.bo4 147030bf3 \([1, 1, 1, 569104, 320913029]\) \(4223169036960119/11647532812500\) \(-56220416207170312500\) \([2]\) \(8257536\) \(2.4732\)  
147030.bo1 147030bf4 \([1, 1, 1, -1411576, -591589627]\) \(64443098670429961/6032611833300\) \(29118265090478939700\) \([2]\) \(8257536\) \(2.4732\)  

Rank

sage: E.rank()
 

The elliptic curves in class 147030bf have rank \(1\).

Complex multiplication

The elliptic curves in class 147030bf do not have complex multiplication.

Modular form 147030.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 4 q^{7} + q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} + 4 q^{14} + q^{15} + q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.