# Properties

 Label 320.c Number of curves $4$ Conductor $320$ CM no Rank $1$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 320.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
320.c1 320b3 $$[0, 0, 0, -428, -3408]$$ $$132304644/5$$ $$327680$$ $$$$ $$64$$ $$0.14436$$
320.c2 320b2 $$[0, 0, 0, -28, -48]$$ $$148176/25$$ $$409600$$ $$[2, 2]$$ $$32$$ $$-0.20221$$
320.c3 320b1 $$[0, 0, 0, -8, 8]$$ $$55296/5$$ $$5120$$ $$$$ $$16$$ $$-0.54879$$ $$\Gamma_0(N)$$-optimal
320.c4 320b4 $$[0, 0, 0, 52, -272]$$ $$237276/625$$ $$-40960000$$ $$$$ $$64$$ $$0.14436$$

## Rank

sage: E.rank()

The elliptic curves in class 320.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 320.c do not have complex multiplication.

## Modular form320.2.a.c

sage: E.q_eigenform(10)

$$q - q^{5} - 4 q^{7} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 