# Properties

 Label 4620.n Number of curves $2$ Conductor $4620$ CM no Rank $1$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 4620.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4620.n1 4620n1 $$[0, 1, 0, -2245, 83975]$$ $$-4890195460096/9282994875$$ $$-2376446688000$$ $$$$ $$7776$$ $$1.0645$$ $$\Gamma_0(N)$$-optimal
4620.n2 4620n2 $$[0, 1, 0, 19355, -1788745]$$ $$3132137615458304/7250937873795$$ $$-1856240095691520$$ $$[]$$ $$23328$$ $$1.6138$$

## Rank

sage: E.rank()

The elliptic curves in class 4620.n have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4620.n do not have complex multiplication.

## Modular form4620.2.a.n

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{7} + q^{9} - q^{11} - 4 q^{13} + q^{15} + 3 q^{17} - 7 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 