# Properties

 Label 3450.z Number of curves $2$ Conductor $3450$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 3450.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.z1 3450v2 $$[1, 0, 0, -79301438, -268415348508]$$ $$3529773792266261468365081/50841342773437500000$$ $$794395980834960937500000$$ $$$$ $$829440$$ $$3.3900$$
3450.z2 3450v1 $$[1, 0, 0, -569438, -11355368508]$$ $$-1306902141891515161/3564268498800000000$$ $$-55691695293750000000000$$ $$$$ $$414720$$ $$3.0435$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3450.2.a.z

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 2q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} + 2q^{13} + 2q^{14} + q^{16} + q^{18} + 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 