# Properties

 Label 1083.a Number of curves $4$ Conductor $1083$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 1083.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1083.a1 1083b3 $$[1, 1, 1, -36649, -2715724]$$ $$115714886617/1539$$ $$72403610859$$ $$[2]$$ $$2160$$ $$1.2272$$
1083.a2 1083b2 $$[1, 1, 1, -2354, -40714]$$ $$30664297/3249$$ $$152852067369$$ $$[2, 2]$$ $$1080$$ $$0.88064$$
1083.a3 1083b1 $$[1, 1, 1, -549, 4050]$$ $$389017/57$$ $$2681615217$$ $$[4]$$ $$540$$ $$0.53406$$ $$\Gamma_0(N)$$-optimal
1083.a4 1083b4 $$[1, 1, 1, 3061, -194500]$$ $$67419143/390963$$ $$-18393198773403$$ $$[2]$$ $$2160$$ $$1.2272$$

## Rank

sage: E.rank()

The elliptic curves in class 1083.a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1083.a do not have complex multiplication.

## Modular form1083.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} + 3 q^{8} + q^{9} + 2 q^{10} + q^{12} - 6 q^{13} + 2 q^{15} - q^{16} - 6 q^{17} - q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.