Properties

Label 930.i
Number of curves $2$
Conductor $930$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 930.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.i1 930i2 \([1, 0, 1, -523, -4642]\) \(-15777367606441/3574920\) \(-3574920\) \([]\) \(360\) \(0.24960\)  
930.i2 930i1 \([1, 0, 1, 2, -22]\) \(1685159/209250\) \(-209250\) \([3]\) \(120\) \(-0.29970\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 930.i have rank \(0\).

Complex multiplication

The elliptic curves in class 930.i do not have complex multiplication.

Modular form 930.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 3 q^{11} + q^{12} + 2 q^{13} + q^{14} + q^{15} + q^{16} - q^{18} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.