Properties

Label 119130u
Number of curves $6$
Conductor $119130$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 119130u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119130.s6 119130u1 \([1, 0, 1, 92047, -1013884]\) \(1833318007919/1070530560\) \(-50364053332623360\) \([2]\) \(1327104\) \(1.8943\) \(\Gamma_0(N)\)-optimal
119130.s5 119130u2 \([1, 0, 1, -370033, -8222332]\) \(119102750067601/68309049600\) \(3213659418704697600\) \([2, 2]\) \(2654208\) \(2.2408\)  
119130.s3 119130u3 \([1, 0, 1, -3864513, 2911765156]\) \(135670761487282321/643043610000\) \(30252553153870410000\) \([2, 2]\) \(5308416\) \(2.5874\)  
119130.s2 119130u4 \([1, 0, 1, -4268833, -3387702172]\) \(182864522286982801/463015182960\) \(21782957198729387760\) \([2]\) \(5308416\) \(2.5874\)  
119130.s4 119130u5 \([1, 0, 1, -1879013, 5900339756]\) \(-15595206456730321/310672490129100\) \(-14615861000587313237100\) \([2]\) \(10616832\) \(2.9340\)  
119130.s1 119130u6 \([1, 0, 1, -61761693, 186816367708]\) \(553808571467029327441/12529687500\) \(589470187092187500\) \([2]\) \(10616832\) \(2.9340\)  

Rank

sage: E.rank()
 

The elliptic curves in class 119130u have rank \(1\).

Complex multiplication

The elliptic curves in class 119130u do not have complex multiplication.

Modular form 119130.2.a.u

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.