# Properties

 Label 369600.qn Number of curves $2$ Conductor $369600$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("qn1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.qn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.qn1 369600qn2 $$[0, 1, 0, -20993, -1175457]$$ $$31226116949/71148$$ $$2331377664000$$ $$[2]$$ $$983040$$ $$1.2546$$
369600.qn2 369600qn1 $$[0, 1, 0, -1793, -4257]$$ $$19465109/11088$$ $$363331584000$$ $$[2]$$ $$491520$$ $$0.90804$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 369600.qn do not have complex multiplication.

## Modular form 369600.2.a.qn

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.