# Properties

 Label 1083c Number of curves $2$ Conductor $1083$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 1083c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1083.d2 1083c1 $$[0, -1, 1, 7100, 260625]$$ $$841232384/1121931$$ $$-52782232316211$$ $$[]$$ $$4320$$ $$1.3189$$ $$\Gamma_0(N)$$-optimal
1083.d1 1083c2 $$[0, -1, 1, -1584910, 768519165]$$ $$-9358714467168256/22284891$$ $$-1048412330083971$$ $$[]$$ $$21600$$ $$2.1236$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1083.2.a.c

sage: E.q_eigenform(10)

$$q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 3 q^{7} + q^{9} + 2 q^{10} - 3 q^{11} - 2 q^{12} + 6 q^{13} + 6 q^{14} - q^{15} - 4 q^{16} + 3 q^{17} + 2 q^{18} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.