Properties

Label 6930.s
Number of curves $2$
Conductor $6930$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6930.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.s1 6930w2 \([1, -1, 1, -7628, -243169]\) \(67324767141241/3368750000\) \(2455818750000\) \([2]\) \(12288\) \(1.1362\)  
6930.s2 6930w1 \([1, -1, 1, 292, -15073]\) \(3789119879/135520000\) \(-98794080000\) \([2]\) \(6144\) \(0.78961\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6930.s have rank \(1\).

Complex multiplication

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

Modular form 6930.2.a.s

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.