# Properties

 Label 6930bl Number of curves 8 Conductor 6930 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.bl1")
sage: E.isogeny_class()

## Elliptic curves in class 6930bl

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.bl6 6930bl1 [1, -1, 1, -2578802, -1593306511] 2 110592 $$\Gamma_0(N)$$-optimal
6930.bl5 6930bl2 [1, -1, 1, -2581682, -1589567119] 4 221184
6930.bl4 6930bl3 [1, -1, 1, -2751737, -1367291239] 6 331776
6930.bl3 6930bl4 [1, -1, 1, -3939962, 265300049] 2 442368
6930.bl7 6930bl5 [1, -1, 1, -1269482, -3205147759] 2 442368
6930.bl2 6930bl6 [1, -1, 1, -14548217, 20191955609] 12 663552
6930.bl1 6930bl7 [1, -1, 1, -229211897, 1335736852121] 6 1327104
6930.bl8 6930bl8 [1, -1, 1, 11371783, 84297299609] 6 1327104

## Rank

sage: E.rank()

The elliptic curves in class 6930bl have rank $$0$$.

## Modular form6930.2.a.bl

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.