# Properties

 Label 64400bs Number of curves $2$ Conductor $64400$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

## Elliptic curves in class 64400bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.ch2 64400bs1 $$[0, -1, 0, 13792, -2937088]$$ $$4533086375/60669952$$ $$-3882876928000000$$ $$$$ $$387072$$ $$1.6720$$ $$\Gamma_0(N)$$-optimal
64400.ch1 64400bs2 $$[0, -1, 0, -242208, -42873088]$$ $$24553362849625/1755162752$$ $$112330416128000000$$ $$$$ $$774144$$ $$2.0186$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.bs

sage: E.q_eigenform(10)

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