Properties

Label 179088cd
Number of curves $4$
Conductor $179088$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 179088cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
179088.i4 179088cd1 \([0, -1, 0, 636, -2592]\) \(110961434288/73773063\) \(-18885904128\) \([2]\) \(122880\) \(0.66057\) \(\Gamma_0(N)\)-optimal
179088.i3 179088cd2 \([0, -1, 0, -2744, -18816]\) \(2232206341348/1127549241\) \(1154610422784\) \([2, 2]\) \(245760\) \(1.0071\)  
179088.i2 179088cd3 \([0, -1, 0, -24064, 1430944]\) \(752515177946114/8396328213\) \(17195680180224\) \([2]\) \(491520\) \(1.3537\)  
179088.i1 179088cd4 \([0, -1, 0, -35504, -2560992]\) \(2416784053495394/2314298259\) \(4739682834432\) \([2]\) \(491520\) \(1.3537\)  

Rank

sage: E.rank()
 

The elliptic curves in class 179088cd have rank \(1\).

Complex multiplication

The elliptic curves in class 179088cd do not have complex multiplication.

Modular form 179088.2.a.cd

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} - q^{7} + q^{9} - q^{13} + 2 q^{15} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.