# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("wz1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.wz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.wz1 369600wz2 $$[0, 1, 0, -3626257313, -22549816971297]$$ $$160934676078320454012702173/86430430219822569086976$$ $$2832152337443145943842029568000$$ $$$$ $$644087808$$ $$4.5344$$
369600.wz2 369600wz1 $$[0, 1, 0, 869512287, -2763934961697]$$ $$2218712073897830722499107/1384711926834951880704$$ $$-45374240418527703226908672000$$ $$$$ $$322043904$$ $$4.1878$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.wz

sage: E.q_eigenform(10)

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

## 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. 