# Properties

 Label 46800bh Number of curves $2$ Conductor $46800$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 46800bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.h1 46800bh1 $$[0, 0, 0, -750, -3625]$$ $$256000/117$$ $$21323250000$$ $$$$ $$36864$$ $$0.67685$$ $$\Gamma_0(N)$$-optimal
46800.h2 46800bh2 $$[0, 0, 0, 2625, -27250]$$ $$686000/507$$ $$-1478412000000$$ $$$$ $$73728$$ $$1.0234$$

## Rank

sage: E.rank()

The elliptic curves in class 46800bh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 46800bh do not have complex multiplication.

## Modular form 46800.2.a.bh

sage: E.q_eigenform(10)

$$q - 4q^{7} - 2q^{11} + q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 