# Properties

 Label 309168d Number of curves $2$ Conductor $309168$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 309168d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
309168.d1 309168d1 $$[0, 0, 0, -71263227, -136593274070]$$ $$13403946614821979039929/5057590268826067968$$ $$15101883621270337735360512$$ $$$$ $$121405440$$ $$3.5310$$ $$\Gamma_0(N)$$-optimal
309168.d2 309168d2 $$[0, 0, 0, 222934533, -974762692310]$$ $$410363075617640914325831/374944243169850027552$$ $$-1119577510997281464669831168$$ $$$$ $$242810880$$ $$3.8775$$

## Rank

sage: E.rank()

The elliptic curves in class 309168d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 309168d do not have complex multiplication.

## Modular form 309168.2.a.d

sage: E.q_eigenform(10)

$$q - 4q^{5} + 4q^{7} + 6q^{17} - q^{19} + O(q^{20})$$ ## 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. 