Properties

Label 188760bn
Number of curves $4$
Conductor $188760$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 188760bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.ba4 188760bn1 \([0, -1, 0, -11054116, -19252754684]\) \(-329381898333928144/162600887109375\) \(-73742691883103100000000\) \([2]\) \(20643840\) \(3.0931\) \(\Gamma_0(N)\)-optimal
188760.ba3 188760bn2 \([0, -1, 0, -194066616, -1040389299684]\) \(445574312599094932036/61129333175625\) \(110893406832582042240000\) \([2, 2]\) \(41287680\) \(3.4397\)  
188760.ba2 188760bn3 \([0, -1, 0, -211369616, -843820298484]\) \(287849398425814280018/81784533026485575\) \(296727120103288446428313600\) \([2]\) \(82575360\) \(3.7863\)  
188760.ba1 188760bn4 \([0, -1, 0, -3104963616, -66592625380884]\) \(912446049969377120252018/17177299425\) \(62321937913144166400\) \([2]\) \(82575360\) \(3.7863\)  

Rank

sage: E.rank()
 

The elliptic curves in class 188760bn have rank \(1\).

Complex multiplication

The elliptic curves in class 188760bn do not have complex multiplication.

Modular form 188760.2.a.bn

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + 4 q^{7} + q^{9} - q^{13} + q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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 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.