# Properties

 Label 15600.bq Number of curves $2$ Conductor $15600$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bq1")

sage: E.isogeny_class()

## Elliptic curves in class 15600.bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bq1 15600cy2 $$[0, 1, 0, -145568, 19649268]$$ $$666276475992821/58199166792$$ $$29797973397504000$$ $$$$ $$147456$$ $$1.9017$$
15600.bq2 15600cy1 $$[0, 1, 0, -142368, 20628468]$$ $$623295446073461/5458752$$ $$2794881024000$$ $$$$ $$73728$$ $$1.5551$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15600.2.a.bq

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. 