# Properties

 Label 64400bl Number of curves $2$ Conductor $64400$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 64400bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.e2 64400bl1 $$[0, 1, 0, -5608, -43212]$$ $$304821217/164864$$ $$10551296000000$$ $$[2]$$ $$122880$$ $$1.1899$$ $$\Gamma_0(N)$$-optimal
64400.e1 64400bl2 $$[0, 1, 0, -69608, -7083212]$$ $$582810602977/829472$$ $$53086208000000$$ $$[2]$$ $$245760$$ $$1.5365$$

## Rank

sage: E.rank()

The elliptic curves in class 64400bl have rank $$1$$.

## Complex multiplication

The elliptic curves in class 64400bl do not have complex multiplication.

## Modular form 64400.2.a.bl

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{7} + q^{9} + 2q^{11} + 4q^{13} + 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.