# Properties

 Label 450840l Number of curves $2$ Conductor $450840$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 450840l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.l2 450840l1 $$[0, -1, 0, -96, 236220]$$ $$-4/975$$ $$-24098948889600$$ $$[2]$$ $$946176$$ $$1.2467$$ $$\Gamma_0(N)$$-optimal*
450840.l1 450840l2 $$[0, -1, 0, -57896, 5299500]$$ $$434163602/7605$$ $$375943602677760$$ $$[2]$$ $$1892352$$ $$1.5932$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 450840l1.

## Rank

sage: E.rank()

The elliptic curves in class 450840l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 450840l do not have complex multiplication.

## Modular form 450840.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + 2q^{7} + q^{9} + q^{13} + q^{15} + 6q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.