# Properties

 Label 2280.b Number of curves $4$ Conductor $2280$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2280.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2280.b1 2280a4 $$[0, -1, 0, -2440, 47212]$$ $$784767874322/35625$$ $$72960000$$ $$$$ $$1536$$ $$0.58494$$
2280.b2 2280a3 $$[0, -1, 0, -760, -7220]$$ $$23735908082/1954815$$ $$4003461120$$ $$$$ $$1536$$ $$0.58494$$
2280.b3 2280a2 $$[0, -1, 0, -160, 700]$$ $$445138564/81225$$ $$83174400$$ $$[2, 2]$$ $$768$$ $$0.23837$$
2280.b4 2280a1 $$[0, -1, 0, 20, 52]$$ $$3286064/7695$$ $$-1969920$$ $$$$ $$384$$ $$-0.10820$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2280.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2280.b do not have complex multiplication.

## Modular form2280.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} + 4 q^{11} + 2 q^{13} - q^{15} + 6 q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 