# Properties

 Label 64400.f Number of curves $2$ Conductor $64400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 64400.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.f1 64400m2 $$[0, 1, 0, -732408, -235452812]$$ $$1357792998752738/38897700625$$ $$1244726420000000000$$ $$$$ $$1179648$$ $$2.2504$$
64400.f2 64400m1 $$[0, 1, 0, -107408, 8297188]$$ $$8564808605476/3081640625$$ $$49306250000000000$$ $$$$ $$589824$$ $$1.9038$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 64400.f have rank $$0$$.

## Complex multiplication

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

## Modular form 64400.2.a.f

sage: E.q_eigenform(10)

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