# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 15600.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.br1 15600cg2 $$[0, 1, 0, -53808, 4787028]$$ $$-168256703745625/30371328$$ $$-3110023987200$$ $$[]$$ $$46656$$ $$1.4009$$
15600.br2 15600cg1 $$[0, 1, 0, 192, 22068]$$ $$7604375/2047032$$ $$-209616076800$$ $$[]$$ $$15552$$ $$0.85155$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15600.2.a.br

sage: E.q_eigenform(10)

$$q + q^{3} - 4q^{7} + q^{9} - q^{13} - 5q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 