# Properties

 Label 349830.fj Number of curves $6$ Conductor $349830$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("349830.fj1")

sage: E.isogeny_class()

## Elliptic curves in class 349830.fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
349830.fj1 349830fj4 [1, -1, 1, -167918432, -837478947769] [2] 28311552
349830.fj2 349830fj5 [1, -1, 1, -39287462, 81199588799] [2] 56623104
349830.fj3 349830fj3 [1, -1, 1, -10768712, -12364726201] [2, 2] 28311552
349830.fj4 349830fj2 [1, -1, 1, -10494932, -13083562969] [2, 2] 14155776
349830.fj5 349830fj1 [1, -1, 1, -638852, -215464921] [2] 7077888 $$\Gamma_0(N)$$-optimal
349830.fj6 349830fj6 [1, -1, 1, 13369558, -59926773409] [2] 56623104

## Rank

sage: E.rank()

The elliptic curves in class 349830.fj have rank $$1$$.

## Modular form 349830.2.a.fj

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.