# Properties

 Label 2880.t Number of curves $4$ Conductor $2880$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 2880.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.t1 2880t3 $$[0, 0, 0, -3852, 92016]$$ $$132304644/5$$ $$238878720$$ $$$$ $$2048$$ $$0.69367$$
2880.t2 2880t2 $$[0, 0, 0, -252, 1296]$$ $$148176/25$$ $$298598400$$ $$[2, 2]$$ $$1024$$ $$0.34709$$
2880.t3 2880t1 $$[0, 0, 0, -72, -216]$$ $$55296/5$$ $$3732480$$ $$$$ $$512$$ $$0.00051877$$ $$\Gamma_0(N)$$-optimal
2880.t4 2880t4 $$[0, 0, 0, 468, 7344]$$ $$237276/625$$ $$-29859840000$$ $$$$ $$2048$$ $$0.69367$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2880.2.a.t

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 