# Properties

 Label 11025.bb Number of curves $3$ Conductor $11025$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 11025.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11025.bb1 11025v3 $$[0, 0, 1, -1447950, -701531469]$$ $$-250523582464/13671875$$ $$-18321620086669921875$$ $$[]$$ $$207360$$ $$2.4544$$
11025.bb2 11025v1 $$[0, 0, 1, -14700, 761031]$$ $$-262144/35$$ $$-46903347421875$$ $$[]$$ $$23040$$ $$1.3558$$ $$\Gamma_0(N)$$-optimal
11025.bb3 11025v2 $$[0, 0, 1, 95550, -1940094]$$ $$71991296/42875$$ $$-57456600591796875$$ $$[]$$ $$69120$$ $$1.9051$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 11025.bb do not have complex multiplication.

## Modular form 11025.2.a.bb

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{11} + 5q^{13} + 4q^{16} - 3q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.