# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 64400l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.cb2 64400l1 $$[0, -1, 0, -708, -9088]$$ $$-9826000/3703$$ $$-14812000000$$ $$$$ $$46080$$ $$0.66139$$ $$\Gamma_0(N)$$-optimal
64400.cb1 64400l2 $$[0, -1, 0, -12208, -515088]$$ $$12576878500/1127$$ $$18032000000$$ $$$$ $$92160$$ $$1.0080$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.l

sage: E.q_eigenform(10)

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