# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("hw1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.hw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.hw1 369600hw2 $$[0, -1, 0, -916833, -16718463]$$ $$665863066004/384359283$$ $$49197988224000000000$$ $$[2]$$ $$10321920$$ $$2.4681$$
369600.hw2 369600hw1 $$[0, -1, 0, -646833, -199508463]$$ $$935299949456/2750517$$ $$88016544000000000$$ $$[2]$$ $$5160960$$ $$2.1215$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.hw

sage: E.q_eigenform(10)

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

## 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.