# Properties

 Label 92400hh Number of curves $4$ Conductor $92400$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("hh1")

sage: E.isogeny_class()

## Elliptic curves in class 92400hh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.hs3 92400hh1 $$[0, 1, 0, -66533, -6725562]$$ $$-130287139815424/2250652635$$ $$-562663158750000$$ $$$$ $$497664$$ $$1.6283$$ $$\Gamma_0(N)$$-optimal
92400.hs2 92400hh2 $$[0, 1, 0, -1068908, -425718312]$$ $$33766427105425744/9823275$$ $$39293100000000$$ $$$$ $$995328$$ $$1.9748$$
92400.hs4 92400hh3 $$[0, 1, 0, 257467, -32038062]$$ $$7549996227362816/6152409907875$$ $$-1538102476968750000$$ $$$$ $$1492992$$ $$2.1776$$
92400.hs1 92400hh4 $$[0, 1, 0, -1239908, -280602312]$$ $$52702650535889104/22020583921875$$ $$88082335687500000000$$ $$$$ $$2985984$$ $$2.5241$$

## Rank

sage: E.rank()

The elliptic curves in class 92400hh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 92400hh do not have complex multiplication.

## Modular form 92400.2.a.hh

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 