# Properties

 Label 277350bg Number of curves $2$ Conductor $277350$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 277350bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.bg2 277350bg1 $$[1, 0, 1, -1734401, -590247052]$$ $$5841725401/1857600$$ $$183477562497225000000$$ $$$$ $$12773376$$ $$2.5921$$ $$\Gamma_0(N)$$-optimal
277350.bg1 277350bg2 $$[1, 0, 1, -10979401, 13554602948]$$ $$1481933914201/53916840$$ $$5325436251481955625000$$ $$$$ $$25546752$$ $$2.9386$$

## Rank

sage: E.rank()

The elliptic curves in class 277350bg have rank $$1$$.

## Complex multiplication

The elliptic curves in class 277350bg do not have complex multiplication.

## Modular form 277350.2.a.bg

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - 2q^{7} - q^{8} + q^{9} - 2q^{11} + q^{12} + 2q^{13} + 2q^{14} + q^{16} + 4q^{17} - q^{18} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 