# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1155.m1")

sage: E.isogeny_class()

## Elliptic curves in class 1155.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.m1 1155l3 [1, 0, 1, -575018, 167782133]  7680
1155.m2 1155l2 [1, 0, 1, -35963, 2615681] [2, 2] 3840
1155.m3 1155l4 [1, 0, 1, -21788, 4702241]  7680
1155.m4 1155l1 [1, 0, 1, -3158, 4403]  1920 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1155.2.a.m

sage: E.q_eigenform(10)

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

## 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. 