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Properties

Label 335730.l
Number of curves $4$
Conductor $335730$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 335730.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
335730.l1 335730l4 \([1, 1, 0, -229405038, 1337277331368]\) \(28379906689597370652529/1357352437500\) \(63857841249684937500\) \([2]\) \(52254720\) \(3.2775\)  
335730.l2 335730l3 \([1, 1, 0, -14314018, 20963307172]\) \(-6894246873502147249/47925198774000\) \(-2254683198422949894000\) \([2]\) \(26127360\) \(2.9310\)  
335730.l3 335730l2 \([1, 1, 0, -3079698, 1493595252]\) \(68663623745397169/19216056254400\) \(904036295833808126400\) \([2]\) \(17418240\) \(2.7282\)  
335730.l4 335730l1 \([1, 1, 0, 501422, 153540148]\) \(296354077829711/387386634240\) \(-18224945495445565440\) \([2]\) \(8709120\) \(2.3817\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 335730.l have rank \(0\).

Complex multiplication

The elliptic curves in class 335730.l do not have complex multiplication.

Modular form 335730.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.