# Properties

 Label 119952w Number of curves $2$ Conductor $119952$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 119952w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fo2 119952w1 $$[0, 0, 0, -4179, -134750]$$ $$-31522396/12393$$ $$-3173204450304$$ $$$$ $$221184$$ $$1.1079$$ $$\Gamma_0(N)$$-optimal
119952.fo1 119952w2 $$[0, 0, 0, -72219, -7469462]$$ $$81344187038/7803$$ $$3995887085568$$ $$$$ $$442368$$ $$1.4545$$

## Rank

sage: E.rank()

The elliptic curves in class 119952w have rank $$1$$.

## Complex multiplication

The elliptic curves in class 119952w do not have complex multiplication.

## Modular form 119952.2.a.w

sage: E.q_eigenform(10)

$$q + 2 q^{5} - 6 q^{13} - q^{17} - 8 q^{19} + O(q^{20})$$ ## 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. 