# Properties

 Label 15600.bh Number of curves $2$ Conductor $15600$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 15600.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bh1 15600bu2 $$[0, -1, 0, -3639208, 2463436912]$$ $$666276475992821/58199166792$$ $$465593334336000000000$$ $$[2]$$ $$737280$$ $$2.7064$$
15600.bh2 15600bu1 $$[0, -1, 0, -3559208, 2585676912]$$ $$623295446073461/5458752$$ $$43670016000000000$$ $$[2]$$ $$368640$$ $$2.3598$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15600.bh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 15600.bh do not have complex multiplication.

## Modular form 15600.2.a.bh

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{7} + q^{9} - 2q^{11} - q^{13} - 4q^{17} - 2q^{19} + O(q^{20})$$

## 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.