# Properties

 Label 1155.m Number of curves $4$ Conductor $1155$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("m1")

E.isogeny_class()

## Elliptic curves in class 1155.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.m1 1155l3 $$[1, 0, 1, -575018, 167782133]$$ $$21026497979043461623321/161783881875$$ $$161783881875$$ $$[4]$$ $$7680$$ $$1.7433$$
1155.m2 1155l2 $$[1, 0, 1, -35963, 2615681]$$ $$5143681768032498601/14238434358225$$ $$14238434358225$$ $$[2, 2]$$ $$3840$$ $$1.3967$$
1155.m3 1155l4 $$[1, 0, 1, -21788, 4702241]$$ $$-1143792273008057401/8897444448004035$$ $$-8897444448004035$$ $$[2]$$ $$7680$$ $$1.7433$$
1155.m4 1155l1 $$[1, 0, 1, -3158, 4403]$$ $$3481467828171481/2005331497785$$ $$2005331497785$$ $$[2]$$ $$1920$$ $$1.0501$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1155.2.a.m

sage: E.q_eigenform(10)

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

## 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.