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Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 11830b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.k1 11830b1 \([1, 0, 1, -1681431704, 26537784815206]\) \(-644487634439863642624729/896000\) \(-730894726016000\) \([3]\) \(2695680\) \(3.5014\) \(\Gamma_0(N)\)-optimal
11830.k2 11830b2 \([1, 0, 1, -1680981319, 26552712085642]\) \(-643969879566315506524489/719323136000000000\) \(-586773980361261056000000000\) \([]\) \(8087040\) \(4.0507\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11830.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.