# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 64400bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.bb1 64400bi1 $$[0, 0, 0, -65075, 6387250]$$ $$476196576129/197225$$ $$12622400000000$$ $$[2]$$ $$221184$$ $$1.4758$$ $$\Gamma_0(N)$$-optimal
64400.bb2 64400bi2 $$[0, 0, 0, -55075, 8417250]$$ $$-288673724529/311181605$$ $$-19915622720000000$$ $$[2]$$ $$442368$$ $$1.8224$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.bi

sage: E.q_eigenform(10)

$$q - q^{7} - 3q^{9} - 2q^{11} - 4q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.