# Properties

 Label 44352.bj Number of curves 6 Conductor 44352 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("44352.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 44352.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44352.bj1 44352cf6 [0, 0, 0, -2602956, 1616397424] [2] 655360
44352.bj2 44352cf4 [0, 0, 0, -163596, 24958960] [2, 2] 327680
44352.bj3 44352cf2 [0, 0, 0, -22476, -724880] [2, 2] 163840
44352.bj4 44352cf1 [0, 0, 0, -19596, -1055504] [2] 81920 $$\Gamma_0(N)$$-optimal
44352.bj5 44352cf5 [0, 0, 0, 17844, 77286256] [2] 655360
44352.bj6 44352cf3 [0, 0, 0, 72564, -5248784] [2] 327680

## Rank

sage: E.rank()

The elliptic curves in class 44352.bj have rank $$1$$.

## Modular form 44352.2.a.bj

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - q^{11} - 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.