Properties

Label 930.b
Number of curves $4$
Conductor $930$
CM no
Rank $1$
Graph

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

Elliptic curves in class 930.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.b1 930a3 \([1, 1, 0, -6628, 204952]\) \(32208729120020809/658986840\) \(658986840\) \([2]\) \(1152\) \(0.81173\)  
930.b2 930a2 \([1, 1, 0, -428, 2832]\) \(8702409880009/1120910400\) \(1120910400\) \([2, 2]\) \(576\) \(0.46515\)  
930.b3 930a1 \([1, 1, 0, -108, -432]\) \(141339344329/17141760\) \(17141760\) \([2]\) \(288\) \(0.11858\) \(\Gamma_0(N)\)-optimal
930.b4 930a4 \([1, 1, 0, 652, 16008]\) \(30579142915511/124675335000\) \(-124675335000\) \([2]\) \(1152\) \(0.81173\)  

Rank

sage: E.rank()
 

The elliptic curves in class 930.b have rank \(1\).

Complex multiplication

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

Modular form 930.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 6q^{13} + q^{15} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.