# Properties

 Label 17136.bl Number of curves $4$ Conductor $17136$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 17136.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17136.bl1 17136j4 $$[0, 0, 0, -1632306819, 25383459170018]$$ $$322159999717985454060440834/4250799$$ $$6346408900608$$ $$$$ $$2211840$$ $$3.4403$$
17136.bl2 17136j3 $$[0, 0, 0, -102281619, 394473389042]$$ $$79260902459030376659234/842751810121431609$$ $$1258221710496816420784128$$ $$$$ $$2211840$$ $$3.4403$$
17136.bl3 17136j2 $$[0, 0, 0, -102019179, 396616526570]$$ $$157304700372188331121828/18069292138401$$ $$13488654304147792896$$ $$[2, 2]$$ $$1105920$$ $$3.0937$$
17136.bl4 17136j1 $$[0, 0, 0, -6359799, 6230596790]$$ $$-152435594466395827792/1646846627220711$$ $$-307341104958437969664$$ $$$$ $$552960$$ $$2.7472$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 17136.bl have rank $$1$$.

## Complex multiplication

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

## Modular form 17136.2.a.bl

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{7} + 2q^{13} - q^{17} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 