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Properties

Label 11830.g
Number of curves $2$
Conductor $11830$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 11830.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.g1 11830k2 \([1, -1, 0, -28924, 336480]\) \(1218083778723573/683593750000\) \(1501855468750000\) \([2]\) \(64512\) \(1.6023\)  
11830.g2 11830k1 \([1, -1, 0, -21644, 1229008]\) \(510408052788213/980000000\) \(2153060000000\) \([2]\) \(32256\) \(1.2557\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11830.g have rank \(1\).

Complex multiplication

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

Modular form 11830.2.a.g

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 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.