# Properties

 Label 2880.z Number of curves $4$ Conductor $2880$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2880.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.z1 2880q3 $$[0, 0, 0, -5772, -168784]$$ $$890277128/15$$ $$358318080$$ $$$$ $$2048$$ $$0.77168$$
2880.z2 2880q4 $$[0, 0, 0, -1452, 18704]$$ $$14172488/1875$$ $$44789760000$$ $$$$ $$2048$$ $$0.77168$$
2880.z3 2880q2 $$[0, 0, 0, -372, -2464]$$ $$1906624/225$$ $$671846400$$ $$[2, 2]$$ $$1024$$ $$0.42511$$
2880.z4 2880q1 $$[0, 0, 0, 33, -196]$$ $$85184/405$$ $$-18895680$$ $$$$ $$512$$ $$0.078535$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2880.2.a.z

sage: E.q_eigenform(10)

$$q + q^{5} - 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 