# Properties

 Label 20160fi Number of curves $4$ Conductor $20160$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fi1")

sage: E.isogeny_class()

## Elliptic curves in class 20160fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.ek4 20160fi1 $$[0, 0, 0, -14401407, -20777112344]$$ $$7079962908642659949376/100085966990454375$$ $$4669610875906639320000$$ $$[2]$$ $$1720320$$ $$2.9627$$ $$\Gamma_0(N)$$-optimal
20160.ek2 20160fi2 $$[0, 0, 0, -229635012, -1339384270016]$$ $$448487713888272974160064/91549016015625$$ $$273363897038400000000$$ $$[2, 2]$$ $$3440640$$ $$3.3093$$
20160.ek1 20160fi3 $$[0, 0, 0, -3674160012, -85720602100016]$$ $$229625675762164624948320008/9568125$$ $$228562145280000$$ $$[2]$$ $$6881280$$ $$3.6559$$
20160.ek3 20160fi4 $$[0, 0, 0, -228847692, -1349024531024]$$ $$-55486311952875723077768/801237030029296875$$ $$-19139847615000000000000000$$ $$[4]$$ $$6881280$$ $$3.6559$$

## Rank

sage: E.rank()

The elliptic curves in class 20160fi have rank $$1$$.

## Complex multiplication

The elliptic curves in class 20160fi do not have complex multiplication.

## Modular form 20160.2.a.fi

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 4q^{11} + 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.