# Properties

 Label 2880.r Number of curves $4$ Conductor $2880$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("r1")

E.isogeny_class()

## Elliptic curves in class 2880.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.r1 2880l4 $$[0, 0, 0, -7788, 264368]$$ $$546718898/405$$ $$38698352640$$ $$[2]$$ $$4096$$ $$0.96528$$
2880.r2 2880l3 $$[0, 0, 0, -4908, -130768]$$ $$136835858/1875$$ $$179159040000$$ $$[2]$$ $$4096$$ $$0.96528$$
2880.r3 2880l2 $$[0, 0, 0, -588, 2288]$$ $$470596/225$$ $$10749542400$$ $$[2, 2]$$ $$2048$$ $$0.61871$$
2880.r4 2880l1 $$[0, 0, 0, 132, 272]$$ $$21296/15$$ $$-179159040$$ $$[2]$$ $$1024$$ $$0.27214$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2880.r have rank $$0$$.

## Complex multiplication

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

## Modular form2880.2.a.r

sage: E.q_eigenform(10)

$$q - q^{5} + 4 q^{7} + 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.