# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 64400v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.j2 64400v1 $$[0, 1, 0, 104792, -1892412]$$ $$7953970437500/4703287687$$ $$-75252602992000000$$ $$[2]$$ $$552960$$ $$1.9277$$ $$\Gamma_0(N)$$-optimal
64400.j1 64400v2 $$[0, 1, 0, -424208, -15646412]$$ $$263822189935250/149429406721$$ $$4781741015072000000$$ $$[2]$$ $$1105920$$ $$2.2742$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.v

sage: E.q_eigenform(10)

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

## 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.