# Properties

 Label 64400m Number of curves $2$ Conductor $64400$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 64400m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.f2 64400m1 $$[0, 1, 0, -107408, 8297188]$$ $$8564808605476/3081640625$$ $$49306250000000000$$ $$[2]$$ $$589824$$ $$1.9038$$ $$\Gamma_0(N)$$-optimal
64400.f1 64400m2 $$[0, 1, 0, -732408, -235452812]$$ $$1357792998752738/38897700625$$ $$1244726420000000000$$ $$[2]$$ $$1179648$$ $$2.2504$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.m

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 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.