Properties

Label 154560w
Number of curves $4$
Conductor $154560$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154560w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.gu3 154560w1 \([0, 1, 0, -8135905, -9569257825]\) \(-227196402372228188089/19338934824115200\) \(-5069585730532854988800\) \([2]\) \(8847360\) \(2.9096\) \(\Gamma_0(N)\)-optimal
154560.gu2 154560w2 \([0, 1, 0, -132725985, -588589195617]\) \(986396822567235411402169/6336721794060000\) \(1661133597982064640000\) \([2]\) \(17694720\) \(3.2562\)  
154560.gu4 154560w3 \([0, 1, 0, 48234335, -337640737]\) \(47342661265381757089751/27397579603968000000\) \(-7182111107702587392000000\) \([2]\) \(26542080\) \(3.4589\)  
154560.gu1 154560w4 \([0, 1, 0, -192938145, -2894069025]\) \(3029968325354577848895529/1753440696000000000000\) \(459653957812224000000000000\) \([2]\) \(53084160\) \(3.8055\)  

Rank

sage: E.rank()
 

The elliptic curves in class 154560w have rank \(0\).

Complex multiplication

The elliptic curves in class 154560w do not have complex multiplication.

Modular form 154560.2.a.w

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.