# Properties

 Label 1470.n Number of curves $2$ Conductor $1470$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1470.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1470.n1 1470n1 $$[1, 1, 1, -15, -15]$$ $$1092727/540$$ $$185220$$ $$$$ $$192$$ $$-0.29613$$ $$\Gamma_0(N)$$-optimal
1470.n2 1470n2 $$[1, 1, 1, 55, -43]$$ $$53582633/36450$$ $$-12502350$$ $$$$ $$384$$ $$0.050440$$

## Rank

sage: E.rank()

The elliptic curves in class 1470.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1470.n do not have complex multiplication.

## Modular form1470.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} + 2 q^{13} - q^{15} + q^{16} - 4 q^{17} + q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 