# Properties

 Label 20216.h Number of curves $4$ Conductor $20216$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 20216.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20216.h1 20216b3 [0, 0, 0, -107939, -13649410]  48384
20216.h2 20216b4 [0, 0, 0, -21299, 946542]  48384
20216.h3 20216b2 [0, 0, 0, -6859, -205770] [2, 2] 24192
20216.h4 20216b1 [0, 0, 0, 361, -13718]  12096 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 20216.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 20216.h do not have complex multiplication.

## Modular form 20216.2.a.h

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 3q^{9} - 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 