Properties

Label 6930.w
Number of curves $4$
Conductor $6930$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.w1 6930x3 \([1, -1, 1, -2395013, -1426026283]\) \(2084105208962185000201/31185000\) \(22733865000\) \([2]\) \(98304\) \(1.9908\)  
6930.w2 6930x4 \([1, -1, 1, -162293, -18275659]\) \(648474704552553481/176469171805080\) \(128646026245903320\) \([2]\) \(98304\) \(1.9908\)  
6930.w3 6930x2 \([1, -1, 1, -149693, -22252219]\) \(508859562767519881/62240270400\) \(45373157121600\) \([2, 2]\) \(49152\) \(1.6443\)  
6930.w4 6930x1 \([1, -1, 1, -8573, -406843]\) \(-95575628340361/43812679680\) \(-31939443486720\) \([2]\) \(24576\) \(1.2977\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6930.w have rank \(0\).

Complex multiplication

The elliptic curves in class 6930.w do not have complex multiplication.

Modular form 6930.2.a.w

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + q^{11} + 2 q^{13} - q^{14} + q^{16} + 2 q^{17} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.