# Properties

 Label 128271.m Number of curves 2 Conductor 128271 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("128271.m1")

sage: E.isogeny_class()

## Elliptic curves in class 128271.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
128271.m1 128271e2 [1, 1, 0, -209225, -36636426] [2] 737280
128271.m2 128271e1 [1, 1, 0, -3890, -1359873] [2] 368640 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 128271.m have rank $$0$$.

## Modular form 128271.2.a.m

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.