# Properties

 Label 17457b Number of curves 2 Conductor 17457 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17457.a1")

sage: E.isogeny_class()

## Elliptic curves in class 17457b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17457.a2 17457b1 [1, 1, 1, -12178, 7516934]  84480 $$\Gamma_0(N)$$-optimal
17457.a1 17457b2 [1, 1, 1, -654913, 202137092]  168960

## Rank

sage: E.rank()

The elliptic curves in class 17457b have rank $$0$$.

## Modular form 17457.2.a.a

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 