# Properties

 Label 15210.bq Number of curves $6$ Conductor $15210$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bq1")

sage: E.isogeny_class()

## Elliptic curves in class 15210.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15210.bq1 15210bn5 $$[1, -1, 1, -13711847, 19546461861]$$ $$81025909800741361/11088090$$ $$39016147508906490$$ $$[2]$$ $$688128$$ $$2.5959$$
15210.bq2 15210bn3 $$[1, -1, 1, -1285277, -560081271]$$ $$66730743078481/60937500$$ $$214423447935937500$$ $$[2]$$ $$344064$$ $$2.2493$$
15210.bq3 15210bn4 $$[1, -1, 1, -859397, 303773721]$$ $$19948814692561/231344100$$ $$814040608519160100$$ $$[2, 2]$$ $$344064$$ $$2.2493$$
15210.bq4 15210bn6 $$[1, -1, 1, -174947, 773853981]$$ $$-168288035761/73415764890$$ $$-258331264665730351290$$ $$[2]$$ $$688128$$ $$2.5959$$
15210.bq5 15210bn2 $$[1, -1, 1, -98897, -4380879]$$ $$30400540561/15210000$$ $$53520092604810000$$ $$[2, 2]$$ $$172032$$ $$1.9027$$
15210.bq6 15210bn1 $$[1, -1, 1, 22783, -535791]$$ $$371694959/249600$$ $$-878278442745600$$ $$[4]$$ $$86016$$ $$1.5561$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15210.bq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 15210.bq do not have complex multiplication.

## Modular form 15210.2.a.bq

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.