# Properties

 Label 369600.nz Number of curves $2$ Conductor $369600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("nz1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.nz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.nz1 369600nz2 $$[0, 1, 0, -2073, -37017]$$ $$1925134784/693$$ $$354816000$$ $$$$ $$229376$$ $$0.60951$$
369600.nz2 369600nz1 $$[0, 1, 0, -148, -442]$$ $$45118016/17787$$ $$142296000$$ $$$$ $$114688$$ $$0.26293$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.nz

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 