# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 8280.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.b1 8280c2 $$[0, 0, 0, -12123, -497178]$$ $$9776035692/359375$$ $$7243344000000$$ $$$$ $$13824$$ $$1.2370$$
8280.b2 8280c1 $$[0, 0, 0, 297, -27702]$$ $$574992/66125$$ $$-333193824000$$ $$$$ $$6912$$ $$0.89038$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8280.2.a.b

sage: E.q_eigenform(10)

$$q - q^{5} - 2 q^{7} - 2 q^{13} - 6 q^{17} + O(q^{20})$$

## 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. 