# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 3450.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3450.l1 3450h2 $$[1, 0, 1, -2901, 57448]$$ $$172715635009/7935000$$ $$123984375000$$ $$$$ $$4608$$ $$0.89025$$
3450.l2 3450h1 $$[1, 0, 1, 99, 3448]$$ $$6967871/331200$$ $$-5175000000$$ $$$$ $$2304$$ $$0.54368$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3450.2.a.l

sage: E.q_eigenform(10)

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