# Properties

 Label 2880.w Number of curves $2$ Conductor $2880$ CM no Rank $1$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 2880.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.w1 2880w2 $$[0, 0, 0, -492, 4176]$$ $$3721734/25$$ $$88473600$$ $$$$ $$1024$$ $$0.35956$$
2880.w2 2880w1 $$[0, 0, 0, -12, 144]$$ $$-108/5$$ $$-8847360$$ $$$$ $$512$$ $$0.012990$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2880.w have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2880.w do not have complex multiplication.

## Modular form2880.2.a.w

sage: E.q_eigenform(10)

$$q + q^{5} - 2q^{7} + 2q^{11} - 4q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 