# Properties

 Label 119952.dl Number of curves $2$ Conductor $119952$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dl1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.dl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.dl1 119952ek2 $$[0, 0, 0, -846496560, 9479548208284]$$ $$-1272481306550272000/5865429267$$ $$-309205845521751654427392$$ $$[]$$ $$24675840$$ $$3.7107$$
119952.dl2 119952ek1 $$[0, 0, 0, -6338640, 23318771308]$$ $$-534274048000/4146834123$$ $$-218607248143747242517248$$ $$[]$$ $$8225280$$ $$3.1614$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 119952.dl have rank $$0$$.

## Complex multiplication

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

## Modular form 119952.2.a.dl

sage: E.q_eigenform(10)

$$q - 5q^{13} - q^{17} - q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 