# Properties

 Label 355740bs Number of curves $4$ Conductor $355740$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

## Elliptic curves in class 355740bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355740.bs3 355740bs1 $$[0, -1, 0, -15779045, 24487788690]$$ $$-130287139815424/2250652635$$ $$-7505382063044470152240$$ $$$$ $$29859840$$ $$2.9954$$ $$\Gamma_0(N)$$-optimal
355740.bs2 355740bs2 $$[0, -1, 0, -253502300, 1553618854152]$$ $$33766427105425744/9823275$$ $$524131931076805497600$$ $$$$ $$59719680$$ $$3.3420$$
355740.bs4 355740bs3 $$[0, -1, 0, 61060795, 117304552422]$$ $$7549996227362816/6152409907875$$ $$-20516798660519243588814000$$ $$$$ $$89579520$$ $$3.5448$$
355740.bs1 355740bs4 $$[0, -1, 0, -294056660, 1023422250600]$$ $$52702650535889104/22020583921875$$ $$1174933123058368904076000000$$ $$$$ $$179159040$$ $$3.8913$$

## Rank

sage: E.rank()

The elliptic curves in class 355740bs have rank $$1$$.

## Complex multiplication

The elliptic curves in class 355740bs do not have complex multiplication.

## Modular form 355740.2.a.bs

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 2q^{13} - q^{15} - 6q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 