# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 3450.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.u1 3450y2 $$[1, 0, 0, -6063, -182133]$$ $$1577505447721/838350$$ $$13099218750$$ $$$$ $$6912$$ $$0.89107$$
3450.u2 3450y1 $$[1, 0, 0, -313, -3883]$$ $$-217081801/285660$$ $$-4463437500$$ $$$$ $$3456$$ $$0.54449$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3450.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{11} + q^{12} - 4q^{13} - 4q^{14} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20})$$ ## 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. 