# Properties

 Label 1155.j Number of curves $4$ Conductor $1155$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 1155.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.j1 1155c3 $$[1, 1, 0, -2123, -38142]$$ $$1058993490188089/13182390375$$ $$13182390375$$ $$$$ $$1152$$ $$0.75160$$
1155.j2 1155c2 $$[1, 1, 0, -248, 483]$$ $$1697509118089/833765625$$ $$833765625$$ $$[2, 2]$$ $$576$$ $$0.40502$$
1155.j3 1155c1 $$[1, 1, 0, -203, 1032]$$ $$932288503609/779625$$ $$779625$$ $$$$ $$288$$ $$0.058449$$ $$\Gamma_0(N)$$-optimal
1155.j4 1155c4 $$[1, 1, 0, 907, 4872]$$ $$82375335041831/56396484375$$ $$-56396484375$$ $$$$ $$1152$$ $$0.75160$$

## Rank

sage: E.rank()

The elliptic curves in class 1155.j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1155.j do not have complex multiplication.

## Modular form1155.2.a.j

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} + q^{7} - 3 q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 2 q^{13} + q^{14} + q^{15} - q^{16} + 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 