# Properties

 Label 20160.fi Number of curves $6$ Conductor $20160$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("20160.fi1")

sage: E.isogeny_class()

## Elliptic curves in class 20160.fi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.fi1 20160cm5 [0, 0, 0, -9676812, 11586348016] [2] 393216
20160.fi2 20160cm4 [0, 0, 0, -604812, 181029616] [2, 2] 196608
20160.fi3 20160cm6 [0, 0, 0, -564492, 206205424] [2] 393216
20160.fi4 20160cm3 [0, 0, 0, -213132, -35795216] [2] 196608
20160.fi5 20160cm2 [0, 0, 0, -40332, 2428144] [2, 2] 98304
20160.fi6 20160cm1 [0, 0, 0, 5748, 234736] [2] 49152 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 20160.fi have rank $$0$$.

## Modular form 20160.2.a.fi

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.