# Properties

 Label 16820.c Number of curves 4 Conductor 16820 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("16820.c1")

sage: E.isogeny_class()

## Elliptic curves in class 16820.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16820.c1 16820b3 [0, -1, 0, -34761, -2482414] [2] 36288
16820.c2 16820b4 [0, -1, 0, -30556, -3109800] [2] 72576
16820.c3 16820b1 [0, -1, 0, -1121, 10310] [2] 12096 $$\Gamma_0(N)$$-optimal
16820.c4 16820b2 [0, -1, 0, 3084, 65816] [2] 24192

## Rank

sage: E.rank()

The elliptic curves in class 16820.c have rank $$0$$.

## Modular form 16820.2.a.c

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + 2q^{7} + q^{9} + 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.