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Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 11830f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.m2 11830f1 \([1, 0, 1, 412, 12898]\) \(45924354671/449576960\) \(-75978506240\) \([]\) \(10368\) \(0.76896\) \(\Gamma_0(N)\)-optimal
11830.m1 11830f2 \([1, 0, 1, -3748, -366494]\) \(-34440478374289/322828856000\) \(-54558076664000\) \([]\) \(31104\) \(1.3183\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 11830.2.a.f

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.