# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 2880.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.i1 2880z3 $$[0, 0, 0, -2028, -34832]$$ $$38614472/405$$ $$9674588160$$ $$$$ $$2048$$ $$0.73261$$
2880.i2 2880z2 $$[0, 0, 0, -228, 448]$$ $$438976/225$$ $$671846400$$ $$[2, 2]$$ $$1024$$ $$0.38604$$
2880.i3 2880z1 $$[0, 0, 0, -183, 952]$$ $$14526784/15$$ $$699840$$ $$$$ $$512$$ $$0.039465$$ $$\Gamma_0(N)$$-optimal
2880.i4 2880z4 $$[0, 0, 0, 852, 3472]$$ $$2863288/1875$$ $$-44789760000$$ $$$$ $$2048$$ $$0.73261$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2880.2.a.i

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{11} - 2q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 