# Properties

 Label 64400g Number of curves $4$ Conductor $64400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 64400g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.be4 64400g1 $$[0, 0, 0, 550, -11625]$$ $$73598976/276115$$ $$-69028750000$$ $$$$ $$30720$$ $$0.76264$$ $$\Gamma_0(N)$$-optimal
64400.be3 64400g2 $$[0, 0, 0, -5575, -140250]$$ $$4790692944/648025$$ $$2592100000000$$ $$[2, 2]$$ $$61440$$ $$1.1092$$
64400.be2 64400g3 $$[0, 0, 0, -23075, 1207250]$$ $$84923690436/9794435$$ $$156710960000000$$ $$$$ $$122880$$ $$1.4558$$
64400.be1 64400g4 $$[0, 0, 0, -86075, -9719750]$$ $$4407931365156/100625$$ $$1610000000000$$ $$$$ $$122880$$ $$1.4558$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.g

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 