# Properties

 Label 353925dd Number of curves $6$ Conductor $353925$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("353925.dd1")

sage: E.isogeny_class()

## Elliptic curves in class 353925dd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
353925.dd5 353925dd1 [1, -1, 0, -653967, 292156816] [2] 7864320 $$\Gamma_0(N)$$-optimal
353925.dd4 353925dd2 [1, -1, 0, -11680092, 15364869691] [2, 2] 15728640
353925.dd1 353925dd3 [1, -1, 0, -186872967, 983305504066] [2] 31457280
353925.dd3 353925dd4 [1, -1, 0, -12905217, 11945545816] [2, 2] 31457280
353925.dd6 353925dd5 [1, -1, 0, 36508158, 81371337691] [2] 62914560
353925.dd2 353925dd6 [1, -1, 0, -81920592, -276331675559] [2] 62914560

## Rank

sage: E.rank()

The elliptic curves in class 353925dd have rank $$0$$.

## Modular form 353925.2.a.dd

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 3q^{8} + q^{13} - q^{16} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.