# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 64400ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.o2 64400ce1 $$[0, -1, 0, 366533792, 3011671430912]$$ $$3403656999841015798655/4418852112356605952$$ $$-7070163379770569523200000000$$ $$[]$$ $$26127360$$ $$4.0297$$ $$\Gamma_0(N)$$-optimal
64400.o1 64400ce2 $$[0, -1, 0, -10421306208, 411961124230912]$$ $$-78229436189152112196207745/549794097750525813248$$ $$-879670556400841301196800000000$$ $$[]$$ $$78382080$$ $$4.5790$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.ce

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} - 2q^{9} - 3q^{11} + 2q^{13} + 3q^{17} - 5q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 