# Properties

 Label 3042.n Number of curves $4$ Conductor $3042$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3042.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3042.n1 3042n4 $$[1, -1, 1, -638969, -196432999]$$ $$18013780041269221/9216$$ $$14760465408$$ $$$$ $$19200$$ $$1.7193$$
3042.n2 3042n3 $$[1, -1, 1, -39929, -3062887]$$ $$-4395631034341/3145728$$ $$-5038238859264$$ $$$$ $$9600$$ $$1.3727$$
3042.n3 3042n2 $$[1, -1, 1, -1904, 12575]$$ $$476379541/236196$$ $$378294584148$$ $$$$ $$3840$$ $$0.91459$$
3042.n4 3042n1 $$[1, -1, 1, 436, 1343]$$ $$5735339/3888$$ $$-6227071344$$ $$$$ $$1920$$ $$0.56802$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3042.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3042.n do not have complex multiplication.

## Modular form3042.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + q^{8} + 2 q^{10} - 2 q^{14} + q^{16} - 2 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 