Properties

Label 11830.c
Number of curves $2$
Conductor $11830$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 11830.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.c1 11830d2 \([1, 0, 1, -950629, -332868144]\) \(19683218700810001/1478750000000\) \(7137643808750000000\) \([2]\) \(376320\) \(2.3630\)  
11830.c2 11830d1 \([1, 0, 1, -193509, 26612432]\) \(166021325905681/32614400000\) \(157423479449600000\) \([2]\) \(188160\) \(2.0164\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11830.2.a.c

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.