# Properties

 Label 2280.a Number of curves $4$ Conductor $2280$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 2280.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2280.a1 2280b4 $$[0, -1, 0, -30400, 2050300]$$ $$3034301922374404/1425$$ $$1459200$$ $$[2]$$ $$2048$$ $$0.95645$$
2280.a2 2280b3 $$[0, -1, 0, -2280, 18972]$$ $$1280615525284/601171875$$ $$615600000000$$ $$[2]$$ $$2048$$ $$0.95645$$
2280.a3 2280b2 $$[0, -1, 0, -1900, 32500]$$ $$2964647793616/2030625$$ $$519840000$$ $$[2, 2]$$ $$1024$$ $$0.60988$$
2280.a4 2280b1 $$[0, -1, 0, -95, 732]$$ $$-5988775936/9774075$$ $$-156385200$$ $$[4]$$ $$512$$ $$0.26330$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2280.a have rank $$1$$.

## Complex multiplication

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

## Modular form2280.2.a.a

sage: E.q_eigenform(10)

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

## 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.