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Properties

Label 363726a
Number of curves $2$
Conductor $363726$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 363726a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363726.a1 363726a1 \([1, -1, 0, -98411319, -375732131571]\) \(81615986309045013769/1940350178448\) \(2505900104109026132112\) \([2]\) \(85708800\) \(3.2174\) \(\Gamma_0(N)\)-optimal
363726.a2 363726a2 \([1, -1, 0, -94774059, -404790201711]\) \(-72896809132486734409/12630799532798172\) \(-16312273019469004079752668\) \([2]\) \(171417600\) \(3.5639\)  

Rank

sage: E.rank()
 

The elliptic curves in class 363726a have rank \(0\).

Complex multiplication

The elliptic curves in class 363726a do not have complex multiplication.

Modular form 363726.2.a.a

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