# Properties

 Label 6171.e Number of curves 2 Conductor 6171 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6171.e1")

sage: E.isogeny_class()

## Elliptic curves in class 6171.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6171.e1 6171g2 [0, 1, 1, -7179, 231875] [] 8100
6171.e2 6171g1 [0, 1, 1, 81, 1370] [] 2700 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6171.e have rank $$0$$.

## Modular form6171.2.a.e

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} + 3q^{5} + 4q^{7} + q^{9} - 2q^{12} + q^{13} + 3q^{15} + 4q^{16} + q^{17} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.