# Properties

 Label 119952.fd Number of curves $2$ Conductor $119952$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("fd1")

sage: E.isogeny_class()

## Elliptic curves in class 119952.fd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.fd1 119952gn2 $$[0, 0, 0, -772779, -261012710]$$ $$423564751/867$$ $$104469359939997696$$ $$[2]$$ $$1835008$$ $$2.1520$$
119952.fd2 119952gn1 $$[0, 0, 0, -31899, -6890870]$$ $$-29791/153$$ $$-18435769401176064$$ $$[2]$$ $$917504$$ $$1.8054$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 119952.2.a.fd

sage: E.q_eigenform(10)

$$q + 2q^{5} - 6q^{11} - 4q^{13} + q^{17} + 2q^{19} + O(q^{20})$$

## 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.