Properties

Label 11830.u
Number of curves $3$
Conductor $11830$
CM no
Rank $0$
Graph

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

Elliptic curves in class 11830.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.u1 11830p3 \([1, 0, 0, -8535040381, -321869146096655]\) \(-14245586655234650511684983641/1028175397808386133196800\) \(-4962806263720098463189513011200\) \([]\) \(32006016\) \(4.6396\)  
11830.u2 11830p1 \([1, 0, 0, -97757631, 403390673945]\) \(-21405018343206000779641/2177246093750000000\) \(-10509151040527343750000000\) \([]\) \(3556224\) \(3.5410\) \(\Gamma_0(N)\)-optimal
11830.u3 11830p2 \([1, 0, 0, 602007994, -369966529180]\) \(4998853083179567995470359/2905108466204672000000\) \(-14022403690652906651648000000\) \([]\) \(10668672\) \(4.0903\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11830.u have rank \(0\).

Complex multiplication

The elliptic curves in class 11830.u do not have complex multiplication.

Modular form 11830.2.a.u

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - q^{7} + q^{8} - 2 q^{9} - q^{10} + 3 q^{11} + q^{12} - q^{14} - q^{15} + q^{16} + 6 q^{17} - 2 q^{18} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.