# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 15600bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.y2 15600bh1 $$[0, -1, 0, 1592, 67312]$$ $$6967871/35100$$ $$-2246400000000$$ $$[2]$$ $$27648$$ $$1.0522$$ $$\Gamma_0(N)$$-optimal
15600.y1 15600bh2 $$[0, -1, 0, -18408, 867312]$$ $$10779215329/1232010$$ $$78848640000000$$ $$[2]$$ $$55296$$ $$1.3988$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15600.2.a.bh

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} - 4q^{11} + q^{13} - 8q^{17} + 6q^{19} + O(q^{20})$$

## 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.