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Properties

Label 358662.y
Number of curves $2$
Conductor $358662$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 358662.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
358662.y1 358662y2 \([1, 0, 0, -3767020, 31230058268]\) \(-39934705050538129/2823126576537804\) \(-417924052517300357247756\) \([]\) \(44008272\) \(3.2122\)  
358662.y2 358662y1 \([1, 0, 0, -878680, -319279552]\) \(-506814405937489/4048994304\) \(-599396471348576256\) \([]\) \(6286896\) \(2.2392\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 358662.y have rank \(0\).

Complex multiplication

The elliptic curves in class 358662.y do not have complex multiplication.

Modular form 358662.2.a.y

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + 2 q^{11} + q^{12} + 7 q^{13} - q^{14} + q^{15} + q^{16} + 3 q^{17} + q^{18} - 6 q^{19} + O(q^{20})\) 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.