# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 64400ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
64400.bd2 64400ba1 $$[0, 0, 0, -356075, 110932250]$$ $$-78013216986489/37918720000$$ $$-2426798080000000000$$ $$$$ $$774144$$ $$2.2332$$ $$\Gamma_0(N)$$-optimal
64400.bd1 64400ba2 $$[0, 0, 0, -6244075, 6004820250]$$ $$420676324562824569/56350000000$$ $$3606400000000000000$$ $$$$ $$1548288$$ $$2.5798$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 64400.2.a.ba

sage: E.q_eigenform(10)

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