# Properties

 Label 8280.h Number of curves $2$ Conductor $8280$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("h1")

E.isogeny_class()

## Elliptic curves in class 8280.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.h1 8280b2 $$[0, 0, 0, -243, -658]$$ $$28697814/13225$$ $$731289600$$ $$[2]$$ $$2560$$ $$0.39559$$
8280.h2 8280b1 $$[0, 0, 0, -123, 518]$$ $$7443468/115$$ $$3179520$$ $$[2]$$ $$1280$$ $$0.049019$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8280.h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8280.h do not have complex multiplication.

## Modular form8280.2.a.h

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.