# Properties

 Label 8880.f Number of curves $2$ Conductor $8880$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 8880.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8880.f1 8880o2 $$[0, -1, 0, -113416, 14757616]$$ $$-39390416456458249/56832000000$$ $$-232783872000000$$ $$[]$$ $$51840$$ $$1.6592$$
8880.f2 8880o1 $$[0, -1, 0, 2024, 94960]$$ $$223759095911/1094104800$$ $$-4481453260800$$ $$[]$$ $$17280$$ $$1.1099$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8880.f have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8880.f do not have complex multiplication.

## Modular form8880.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} - 3q^{11} - 7q^{13} + q^{15} - 3q^{17} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 