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Properties

Label 370146.z
Number of curves $2$
Conductor $370146$
CM no
Rank $0$
Graph

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

Elliptic curves in class 370146.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
370146.z1 370146z2 \([1, 1, 1, -57317555, 13117829759579]\) \(-177010260681338006596129/631757862884385194481594\) \(-74325680810485033745565052506\) \([]\) \(320060160\) \(4.2188\)  
370146.z2 370146z1 \([1, 1, 1, -55249265, -158634697201]\) \(-158531287603583609503489/634774607963040384\) \(-74680597852243738137216\) \([]\) \(45722880\) \(3.2458\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 370146.z have rank \(0\).

Complex multiplication

The elliptic curves in class 370146.z do not have complex multiplication.

Modular form 370146.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} - q^{15} + q^{16} - 4 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.