# Properties

 Label 3150.bo Number of curves $6$ Conductor $3150$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3150.bo1")

sage: E.isogeny_class()

## Elliptic curves in class 3150.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.bo1 3150bl3 [1, -1, 1, -302405, -63931903] [2] 16384
3150.bo2 3150bl5 [1, -1, 1, -205655, 35603597] [2] 32768
3150.bo3 3150bl4 [1, -1, 1, -23405, -481903] [2, 2] 16384
3150.bo4 3150bl2 [1, -1, 1, -18905, -994903] [2, 2] 8192
3150.bo5 3150bl1 [1, -1, 1, -905, -22903] [2] 4096 $$\Gamma_0(N)$$-optimal
3150.bo6 3150bl6 [1, -1, 1, 86845, -3789403] [2] 32768

## Rank

sage: E.rank()

The elliptic curves in class 3150.bo have rank $$0$$.

## Modular form3150.2.a.bo

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} + 4q^{11} - 6q^{13} + q^{14} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.