# Properties

 Label 15600f Number of curves $4$ Conductor $15600$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 15600f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15600.bf4 15600f1 $$[0, -1, 0, -508, -15488]$$ $$-3631696/24375$$ $$-97500000000$$ $$$$ $$18432$$ $$0.79195$$ $$\Gamma_0(N)$$-optimal
15600.bf3 15600f2 $$[0, -1, 0, -13008, -565488]$$ $$15214885924/38025$$ $$608400000000$$ $$[2, 2]$$ $$36864$$ $$1.1385$$
15600.bf1 15600f3 $$[0, -1, 0, -208008, -36445488]$$ $$31103978031362/195$$ $$6240000000$$ $$$$ $$73728$$ $$1.4851$$
15600.bf2 15600f4 $$[0, -1, 0, -18008, -85488]$$ $$20183398562/11567205$$ $$370150560000000$$ $$$$ $$73728$$ $$1.4851$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 15600.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} + 4q^{7} + q^{9} - 4q^{11} - q^{13} - 6q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 