# Properties

 Label 8349a Number of curves 2 Conductor 8349 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8349.c1")

sage: E.isogeny_class()

## Elliptic curves in class 8349a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8349.c2 8349a1 [1, 1, 0, -2785, 821704]  19200 $$\Gamma_0(N)$$-optimal
8349.c1 8349a2 [1, 1, 0, -149800, 22080073]  38400

## Rank

sage: E.rank()

The elliptic curves in class 8349a have rank $$1$$.

## Modular form8349.2.a.c

sage: E.q_eigenform(10)

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

## 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. 