Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 11830s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.r2 11830s1 \([1, -1, 1, -3657868, 2689157007]\) \(510408052788213/980000000\) \(10392409385540000000\) \([2]\) \(419328\) \(2.5382\) \(\Gamma_0(N)\)-optimal
11830.r1 11830s2 \([1, -1, 1, -4888188, 724582031]\) \(1218083778723573/683593750000\) \(7249169493261718750000\) \([2]\) \(838656\) \(2.8848\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11830.2.a.s

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