# Properties

 Label 3450.n Number of curves $2$ Conductor $3450$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 3450.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.n1 3450p2 $$[1, 1, 1, -13007513, -18274618969]$$ $$-24923353462910020825/341398360424448$$ $$-3333968363520000000000$$ $$[]$$ $$336960$$ $$2.9366$$
3450.n2 3450p1 $$[1, 1, 1, 576862, -125893969]$$ $$2173899265153175/1961845235712$$ $$-19158644880000000000$$ $$[]$$ $$112320$$ $$2.3873$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3450.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3450.n do not have complex multiplication.

## Modular form3450.2.a.n

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 5q^{7} + q^{8} + q^{9} - q^{12} - 2q^{13} - 5q^{14} + q^{16} - 3q^{17} + q^{18} + 2q^{19} + O(q^{20})$$ ## 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. 