# Properties

 Label 43758.n Number of curves $4$ Conductor $43758$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 43758.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.n1 43758t3 $$[1, -1, 1, -29656985, 62160880889]$$ $$3957101249824708884951625/772310238681366528$$ $$563014163998716198912$$ $$[6]$$ $$3649536$$ $$2.9814$$
43758.n2 43758t4 $$[1, -1, 1, -26523545, 75806385401]$$ $$-2830680648734534916567625/1766676274677722124288$$ $$-1287907004240059428605952$$ $$[6]$$ $$7299072$$ $$3.3279$$
43758.n3 43758t1 $$[1, -1, 1, -902930, -213616879]$$ $$111675519439697265625/37528570137307392$$ $$27358327630097088768$$ $$[2]$$ $$1216512$$ $$2.4321$$ $$\Gamma_0(N)$$-optimal
43758.n4 43758t2 $$[1, -1, 1, 2634430, -1478576815]$$ $$2773679829880629422375/2899504554614368272$$ $$-2113738820313874470288$$ $$[2]$$ $$2433024$$ $$2.7786$$

## Rank

sage: E.rank()

The elliptic curves in class 43758.n have rank $$0$$.

## Complex multiplication

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

## Modular form 43758.2.a.n

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels.