Properties

Label 930.c
Number of curves $2$
Conductor $930$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 930.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.c1 930e2 \([1, 1, 0, -47, 99]\) \(11867954041/778410\) \(778410\) \([2]\) \(192\) \(-0.11985\)  
930.c2 930e1 \([1, 1, 0, 3, 9]\) \(1685159/27900\) \(-27900\) \([2]\) \(96\) \(-0.46643\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 930.2.a.c

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