# Properties

 Label 8280.m Number of curves $2$ Conductor $8280$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8280.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.m1 8280d2 $$[0, 0, 0, -1467, -21626]$$ $$12628458252/575$$ $$15897600$$ $$$$ $$2560$$ $$0.45780$$
8280.m2 8280d1 $$[0, 0, 0, -87, -374]$$ $$-10536048/2645$$ $$-18282240$$ $$$$ $$1280$$ $$0.11123$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8280.2.a.m

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 