# Properties

 Label 11025ba Number of curves 6 Conductor 11025 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11025.g1")

sage: E.isogeny_class()

## Elliptic curves in class 11025ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11025.g6 11025ba1 [1, -1, 1, 10795, -97828] [2] 24576 $$\Gamma_0(N)$$-optimal
11025.g5 11025ba2 [1, -1, 1, -44330, -759328] [2, 2] 49152
11025.g2 11025ba3 [1, -1, 1, -540455, -152573578] [2, 2] 98304
11025.g3 11025ba4 [1, -1, 1, -430205, 108057422] [2] 98304
11025.g1 11025ba5 [1, -1, 1, -8643830, -9779383078] [2] 196608
11025.g4 11025ba6 [1, -1, 1, -375080, -247829578] [2] 196608

## Rank

sage: E.rank()

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

## Modular form 11025.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 3q^{8} - 4q^{11} - 2q^{13} - q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.