# Properties

 Label 350064bc Number of curves $2$ Conductor $350064$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 350064bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350064.bc1 350064bc1 $$[0, 0, 0, -434955, -100427078]$$ $$3047678972871625/304559880768$$ $$909410931015155712$$ $$$$ $$4128768$$ $$2.1823$$ $$\Gamma_0(N)$$-optimal
350064.bc2 350064bc2 $$[0, 0, 0, 538485, -486104006]$$ $$5783051584712375/37533175779528$$ $$-112073462346858135552$$ $$$$ $$8257536$$ $$2.5289$$

## Rank

sage: E.rank()

The elliptic curves in class 350064bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 350064bc do not have complex multiplication.

## Modular form 350064.2.a.bc

sage: E.q_eigenform(10)

$$q - 2q^{7} + q^{11} + q^{13} + q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 