# Properties

 Label 369600.hq Number of curves $6$ Conductor $369600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("369600.hq1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.hq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
369600.hq1 369600hq6 [0, -1, 0, -21200033, -37562148063] [2] 25165824
369600.hq2 369600hq4 [0, -1, 0, -1400033, -516348063] [2, 2] 12582912
369600.hq3 369600hq2 [0, -1, 0, -432033, 102203937] [2, 2] 6291456
369600.hq4 369600hq1 [0, -1, 0, -424033, 106419937] [2] 3145728 $$\Gamma_0(N)$$-optimal
369600.hq5 369600hq3 [0, -1, 0, 407967, 450803937] [2] 12582912
369600.hq6 369600hq5 [0, -1, 0, 2911967, -3073364063] [2] 25165824

## Rank

sage: E.rank()

The elliptic curves in class 369600.hq have rank $$0$$.

## Modular form 369600.2.a.hq

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - q^{11} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.