Properties

Label 363090.be
Number of curves $8$
Conductor $363090$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 363090.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
363090.be1 363090be7 \([1, 1, 0, -652331356107, 202791574383463101]\) \(260939746299651996897062684320310569/4502310731746516416000000\) \(529692355279245909825984000000\) \([2]\) \(3057647616\) \(5.2447\)  
363090.be2 363090be6 \([1, 1, 0, -40811356107, 3161971119463101]\) \(63896717795469435410864800310569/264596810010624000000000000\) \(31129550100939902976000000000000\) \([2, 2]\) \(1528823808\) \(4.8982\)  
363090.be3 363090be8 \([1, 1, 0, -21191536587, 6207779369495229]\) \(-8945874824846901999181300606249/136327175537109375000000000000\) \(-16038755874765380859375000000000000\) \([2]\) \(3057647616\) \(5.2447\)  
363090.be4 363090be4 \([1, 1, 0, -8554086972, 241636399716384]\) \(588378042102789360957899335609/126092479227795814426383600\) \(14834654088670949771449604156400\) \([2]\) \(1019215872\) \(4.6954\)  
363090.be5 363090be3 \([1, 1, 0, -3817594827, -4820624893251]\) \(52300395461270777993673352489/30181158775846600704000000\) \(3550783148819576726224896000000\) \([2]\) \(764411904\) \(4.5516\)  
363090.be6 363090be2 \([1, 1, 0, -2740824972, -51932168631216]\) \(19354385182631020519933543609/1297852417956067777440000\) \(152691039120113417948038560000\) \([2, 2]\) \(509607936\) \(4.3489\)  
363090.be7 363090be1 \([1, 1, 0, -2695102092, -53854020157104]\) \(18401835147394456911544300729/91846771642205798400\) \(10805680836933869975961600\) \([2]\) \(254803968\) \(4.0023\) \(\Gamma_0(N)\)-optimal
363090.be8 363090be5 \([1, 1, 0, 2340870948, -222501324864384]\) \(12057794750690459080173411911/188765599666333542693750000\) \(-22208084035144474964376993750000\) \([2]\) \(1019215872\) \(4.6954\)  

Rank

sage: E.rank()
 

The elliptic curves in class 363090.be have rank \(1\).

Complex multiplication

The elliptic curves in class 363090.be do not have complex multiplication.

Modular form 363090.2.a.be

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

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.