# Properties

 Label 6930o Number of curves 8 Conductor 6930 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.q1")
sage: E.isogeny_class()

## Elliptic curves in class 6930o

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.q8 6930o1 [1, -1, 0, 14301, -85995] 2 27648 $$\Gamma_0(N)$$-optimal
6930.q7 6930o2 [1, -1, 0, -57699, -647595] 4 55296
6930.q6 6930o3 [1, -1, 0, -182259, 32927013] 6 82944
6930.q4 6930o4 [1, -1, 0, -675099, -212909715] 2 110592
6930.q5 6930o5 [1, -1, 0, -592299, 174808125] 2 110592
6930.q3 6930o6 [1, -1, 0, -2994759, 1995489513] 12 165888
6930.q2 6930o7 [1, -1, 0, -3073509, 1885066263] 6 331776
6930.q1 6930o8 [1, -1, 0, -47916009, 127676162763] 6 331776

## Rank

sage: E.rank()

The elliptic curves in class 6930o have rank $$1$$.

## Modular form6930.2.a.q

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + q^{11} + 2q^{13} - q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.