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Properties

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

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

Elliptic curves in class 40362b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40362.e2 40362b1 \([1, 1, 0, -6117265, -5149561067]\) \(28524992814753625/3612440788992\) \(3206054497624944279552\) \([2]\) \(2027520\) \(2.8558\) \(\Gamma_0(N)\)-optimal
40362.e1 40362b2 \([1, 1, 0, -94683025, -354647763179]\) \(105771808529903265625/2083934619648\) \(1849499645900934924288\) \([2]\) \(4055040\) \(3.2024\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 40362.2.a.b

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