# Properties

 Label 9280.m Number of curves $2$ Conductor $9280$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("m1")

E.isogeny_class()

## Elliptic curves in class 9280.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9280.m1 9280o1 $$[0, 0, 0, -32, 56]$$ $$3538944/725$$ $$742400$$ $$[2]$$ $$768$$ $$-0.15807$$ $$\Gamma_0(N)$$-optimal
9280.m2 9280o2 $$[0, 0, 0, 68, 336]$$ $$2122416/4205$$ $$-68894720$$ $$[2]$$ $$1536$$ $$0.18850$$

## Rank

sage: E.rank()

The elliptic curves in class 9280.m have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9280.m do not have complex multiplication.

## Modular form9280.2.a.m

sage: E.q_eigenform(10)

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

## 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.