Properties

Label 388080ew
Number of curves $4$
Conductor $388080$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ew1")
 
E.isogeny_class()
 

Elliptic curves in class 388080ew

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.ew3 388080ew1 \([0, 0, 0, -50568, -353633]\) \(281370820608/161767375\) \(8221724597394000\) \([2]\) \(1990656\) \(1.7434\) \(\Gamma_0(N)\)-optimal
388080.ew4 388080ew2 \([0, 0, 0, 201537, -2824262]\) \(1113258734352/648484375\) \(-527340936276000000\) \([2]\) \(3981312\) \(2.0900\)  
388080.ew1 388080ew3 \([0, 0, 0, -2931768, -1932150213]\) \(75216478666752/326095\) \(12082134194277840\) \([2]\) \(5971968\) \(2.2927\)  
388080.ew2 388080ew4 \([0, 0, 0, -2885463, -1996134462]\) \(-4481782160112/310023175\) \(-183786521286672057600\) \([2]\) \(11943936\) \(2.6393\)  

Rank

sage: E.rank()
 

The elliptic curves in class 388080ew have rank \(0\).

Complex multiplication

The elliptic curves in class 388080ew do not have complex multiplication.

Modular form 388080.2.a.ew

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{11} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.