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Properties

Label 364650.cm
Number of curves $2$
Conductor $364650$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 364650.cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
364650.cm1 364650cm1 \([1, 0, 1, -136076, -14880202]\) \(142670337598277/33663817044\) \(65749642664062500\) \([2]\) \(3440640\) \(1.9387\) \(\Gamma_0(N)\)-optimal
364650.cm2 364650cm2 \([1, 0, 1, 317674, -92925202]\) \(1815267585851803/2961534890886\) \(-5784247833761718750\) \([2]\) \(6881280\) \(2.2852\)  

Rank

sage: E.rank()
 

The elliptic curves in class 364650.cm have rank \(1\).

Complex multiplication

The elliptic curves in class 364650.cm do not have complex multiplication.

Modular form 364650.2.a.cm

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