Properties

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

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 388080z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388080.z3 388080z1 \([0, 0, 0, -6445803, -6325560038]\) \(-84309998289049/414124480\) \(-145481114667999559680\) \([2]\) \(15925248\) \(2.7170\) \(\Gamma_0(N)\)-optimal
388080.z2 388080z2 \([0, 0, 0, -103254123, -403839883622]\) \(346553430870203929/8300600\) \(2915984441231769600\) \([2]\) \(31850496\) \(3.0636\)  
388080.z4 388080z3 \([0, 0, 0, 16027557, -33584362742]\) \(1296134247276791/2137096192000\) \(-750757685623649206272000\) \([2]\) \(47775744\) \(3.2664\)  
388080.z1 388080z4 \([0, 0, 0, -110415963, -344610133238]\) \(423783056881319689/99207416000000\) \(34851369962509664256000000\) \([2]\) \(95551488\) \(3.6129\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 388080.2.a.z

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