# Properties

 Label 1600.c Number of curves $4$ Conductor $1600$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 1600.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1600.c1 1600g3 $$[0, 1, 0, -4133, -103637]$$ $$488095744/125$$ $$2000000000$$ $$$$ $$1152$$ $$0.77065$$
1600.c2 1600g4 $$[0, 1, 0, -3633, -129137]$$ $$-20720464/15625$$ $$-4000000000000$$ $$$$ $$2304$$ $$1.1172$$
1600.c3 1600g1 $$[0, 1, 0, -133, 363]$$ $$16384/5$$ $$80000000$$ $$$$ $$384$$ $$0.22134$$ $$\Gamma_0(N)$$-optimal
1600.c4 1600g2 $$[0, 1, 0, 367, 2863]$$ $$21296/25$$ $$-6400000000$$ $$$$ $$768$$ $$0.56792$$

## Rank

sage: E.rank()

The elliptic curves in class 1600.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1600.c do not have complex multiplication.

## Modular form1600.2.a.c

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 