Properties

Label 36414.w
Number of curves $2$
Conductor $36414$
CM no
Rank $0$
Graph

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

Elliptic curves in class 36414.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36414.w1 36414p1 \([1, -1, 0, -1975947, -1009423675]\) \(9869198625/614656\) \(53137356615966083328\) \([2]\) \(1114112\) \(2.5364\) \(\Gamma_0(N)\)-optimal
36414.w2 36414p2 \([1, -1, 0, 1561413, -4230543691]\) \(4869777375/92236816\) \(-7973924577183410379408\) \([2]\) \(2228224\) \(2.8829\)  

Rank

sage: E.rank()
 

The elliptic curves in class 36414.w have rank \(0\).

Complex multiplication

The elliptic curves in class 36414.w do not have complex multiplication.

Modular form 36414.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} + 2 q^{13} + q^{14} + q^{16} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.