# Properties

 Label 33600.he Number of curves $6$ Conductor $33600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33600.he1")

sage: E.isogeny_class()

## Elliptic curves in class 33600.he

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.he1 33600gt6 [0, 1, 0, -26880033, 53631540063] [2] 1179648
33600.he2 33600gt4 [0, 1, 0, -1680033, 837540063] [2, 2] 589824
33600.he3 33600gt5 [0, 1, 0, -1568033, 954132063] [2] 1179648
33600.he4 33600gt3 [0, 1, 0, -592033, -165915937] [2] 589824
33600.he5 33600gt2 [0, 1, 0, -112033, 11204063] [2, 2] 294912
33600.he6 33600gt1 [0, 1, 0, 15967, 1092063] [2] 147456 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 33600.he have rank $$0$$.

## Modular form 33600.2.a.he

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.