# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("dn1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.dn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.dn1 119952s1 $$[0, 0, 0, -21315, 1184722]$$ $$12194500/153$$ $$13437149709312$$ $$$$ $$184320$$ $$1.3285$$ $$\Gamma_0(N)$$-optimal
119952.dn2 119952s2 $$[0, 0, 0, -3675, 3086314]$$ $$-31250/23409$$ $$-4111767811049472$$ $$$$ $$368640$$ $$1.6751$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 119952.2.a.dn

sage: E.q_eigenform(10)

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