# Properties

 Label 369600.hb Number of curves $2$ Conductor $369600$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("hb1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.hb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.hb1 369600hb1 $$[0, -1, 0, -224533, -84648563]$$ $$-4890195460096/9282994875$$ $$-2376446688000000000$$ $$[]$$ $$5971968$$ $$2.2158$$ $$\Gamma_0(N)$$-optimal
369600.hb2 369600hb2 $$[0, -1, 0, 1935467, 1794551437]$$ $$3132137615458304/7250937873795$$ $$-1856240095691520000000$$ $$[]$$ $$17915904$$ $$2.7651$$

## Rank

sage: E.rank()

The elliptic curves in class 369600.hb have rank $$1$$.

## Complex multiplication

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

## Modular form 369600.2.a.hb

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.