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Properties

Label 40362r
Number of curves $2$
Conductor $40362$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 40362r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40362.r1 40362r1 \([1, 0, 1, -182130, 26323204]\) \(752825955673/97993728\) \(86969794314912768\) \([2]\) \(460800\) \(1.9788\) \(\Gamma_0(N)\)-optimal
40362.r2 40362r2 \([1, 0, 1, 279150, 138137476]\) \(2710620272807/10853826144\) \(-9632810655734036064\) \([2]\) \(921600\) \(2.3253\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40362r have rank \(0\).

Complex multiplication

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

Modular form 40362.2.a.r

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