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Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 40362.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40362.b1 40362h2 \([1, 1, 0, -217538226, -1235028586176]\) \(43060118286713527/729137052\) \(19278108158225523281892\) \([2]\) \(7999488\) \(3.4061\)  
40362.b2 40362h1 \([1, 1, 0, -13171966, -20561649500]\) \(-9559173016567/1372257936\) \(-36281981334822246835056\) \([2]\) \(3999744\) \(3.0595\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 40362.2.a.b

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