# Properties

 Label 43758u Number of curves $2$ Conductor $43758$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 43758u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.r1 43758u1 $$[1, -1, 1, -27185, 1575969]$$ $$3047678972871625/304559880768$$ $$222024153079872$$ $$$$ $$172032$$ $$1.4892$$ $$\Gamma_0(N)$$-optimal
43758.r2 43758u2 $$[1, -1, 1, 33655, 7586961]$$ $$5783051584712375/37533175779528$$ $$-27361685143275912$$ $$$$ $$344064$$ $$1.8358$$

## Rank

sage: E.rank()

The elliptic curves in class 43758u have rank $$1$$.

## Complex multiplication

The elliptic curves in class 43758u do not have complex multiplication.

## Modular form 43758.2.a.u

sage: E.q_eigenform(10)

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