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Properties

Label 40362o
Number of curves $2$
Conductor $40362$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 40362o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40362.t2 40362o1 \([1, 0, 1, -10454259, -13010977586]\) \(142374842119352809/2700952128\) \(2397104955804783168\) \([2]\) \(2764800\) \(2.6504\) \(\Gamma_0(N)\)-optimal
40362.t1 40362o2 \([1, 0, 1, -10800219, -12103870466]\) \(156982476866335849/19545027428808\) \(17346283788313065442248\) \([2]\) \(5529600\) \(2.9970\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40362o have rank \(1\).

Complex multiplication

The elliptic curves in class 40362o do not have complex multiplication.

Modular form 40362.2.a.o

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