# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 64400.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.l1 64400bu2 $$[0, 1, 0, -2528, 111988]$$ $$-17455277065/43606528$$ $$-4465308467200$$ $$[]$$ $$124416$$ $$1.1152$$
64400.l2 64400bu1 $$[0, 1, 0, 272, -3372]$$ $$21653735/63112$$ $$-6462668800$$ $$[]$$ $$41472$$ $$0.56587$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.l

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.