# Properties

 Label 350658ba Number of curves $2$ Conductor $350658$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 350658ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.ba2 350658ba1 $$[1, -1, 0, 37548, 13163728]$$ $$4533086375/60669952$$ $$-78353299688767488$$ $$$$ $$3440640$$ $$1.9224$$ $$\Gamma_0(N)$$-optimal
350658.ba1 350658ba2 $$[1, -1, 0, -659412, 193118800]$$ $$24553362849625/1755162752$$ $$2266736474589890688$$ $$$$ $$6881280$$ $$2.2690$$

## Rank

sage: E.rank()

The elliptic curves in class 350658ba have rank $$0$$.

## Complex multiplication

The elliptic curves in class 350658ba do not have complex multiplication.

## Modular form 350658.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} + q^{14} + q^{16} + 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 