Properties

Label 159120cs
Number of curves $4$
Conductor $159120$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cs1")
 
E.isogeny_class()
 

Elliptic curves in class 159120cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.r3 159120cs1 \([0, 0, 0, -10968, -444433]\) \(-337770946363392/2051393825\) \(-886202132400\) \([2]\) \(221184\) \(1.1318\) \(\Gamma_0(N)\)-optimal
159120.r2 159120cs2 \([0, 0, 0, -175743, -28357318]\) \(86846853774358512/3174665\) \(21943284480\) \([2]\) \(442368\) \(1.4784\)  
159120.r4 159120cs3 \([0, 0, 0, 29592, -2370357]\) \(9099874271232/12973390625\) \(-4085683962750000\) \([2]\) \(663552\) \(1.6811\)  
159120.r1 159120cs4 \([0, 0, 0, -189783, -23561982]\) \(150025256088048/39223549625\) \(197641504580832000\) \([2]\) \(1327104\) \(2.0277\)  

Rank

sage: E.rank()
 

The elliptic curves in class 159120cs have rank \(1\).

Complex multiplication

The elliptic curves in class 159120cs do not have complex multiplication.

Modular form 159120.2.a.cs

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.