# Properties

 Label 11025x Number of curves 4 Conductor 11025 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11025.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 11025x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11025.bd3 11025x1 [1, -1, 0, -27792, 1696491] [2] 36864 $$\Gamma_0(N)$$-optimal
11025.bd2 11025x2 [1, -1, 0, -82917, -7068384] [2, 2] 73728
11025.bd1 11025x3 [1, -1, 0, -1240542, -531472509] [2] 147456
11025.bd4 11025x4 [1, -1, 0, 192708, -44277759] [2] 147456

## Rank

sage: E.rank()

The elliptic curves in class 11025x have rank $$1$$.

## Modular form 11025.2.a.bd

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.