# Properties

 Label 2880.b Number of curves $4$ Conductor $2880$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("b1")

E.isogeny_class()

## Elliptic curves in class 2880.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.b1 2880bc3 $$[0, 0, 0, -7788, -264368]$$ $$546718898/405$$ $$38698352640$$ $$[2]$$ $$4096$$ $$0.96528$$
2880.b2 2880bc4 $$[0, 0, 0, -4908, 130768]$$ $$136835858/1875$$ $$179159040000$$ $$[2]$$ $$4096$$ $$0.96528$$
2880.b3 2880bc2 $$[0, 0, 0, -588, -2288]$$ $$470596/225$$ $$10749542400$$ $$[2, 2]$$ $$2048$$ $$0.61871$$
2880.b4 2880bc1 $$[0, 0, 0, 132, -272]$$ $$21296/15$$ $$-179159040$$ $$[2]$$ $$1024$$ $$0.27214$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2880.2.a.b

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.