# Properties

 Label 17136bl Number of curves $4$ Conductor $17136$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 17136bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17136.bk4 17136bl1 $$[0, 0, 0, 141, 174130]$$ $$103823/4386816$$ $$-13098962386944$$ $$[2]$$ $$36864$$ $$1.1959$$ $$\Gamma_0(N)$$-optimal
17136.bk3 17136bl2 $$[0, 0, 0, -45939, 3722290]$$ $$3590714269297/73410624$$ $$219202948694016$$ $$[2, 2]$$ $$73728$$ $$1.5424$$
17136.bk2 17136bl3 $$[0, 0, 0, -97779, -6220622]$$ $$34623662831857/14438442312$$ $$43112957728555008$$ $$[2]$$ $$147456$$ $$1.8890$$
17136.bk1 17136bl4 $$[0, 0, 0, -731379, 240747442]$$ $$14489843500598257/6246072$$ $$18650671054848$$ $$[2]$$ $$147456$$ $$1.8890$$

## Rank

sage: E.rank()

The elliptic curves in class 17136bl have rank $$0$$.

## Complex multiplication

The elliptic curves in class 17136bl do not have complex multiplication.

## Modular form 17136.2.a.bl

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{7} - 6q^{13} - q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.