# Properties

 Label 129360fb Number of curves $2$ Conductor $129360$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fb1")

sage: E.isogeny_class()

## Elliptic curves in class 129360fb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129360.cw2 129360fb1 $$[0, -1, 0, -1045, 41140]$$ $$-67108864/343035$$ $$-645723595440$$ $$[2]$$ $$184320$$ $$0.95045$$ $$\Gamma_0(N)$$-optimal
129360.cw1 129360fb2 $$[0, -1, 0, -25300, 1554652]$$ $$59466754384/121275$$ $$3652577913600$$ $$[2]$$ $$368640$$ $$1.2970$$

## Rank

sage: E.rank()

The elliptic curves in class 129360fb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 129360fb do not have complex multiplication.

## Modular form 129360.2.a.fb

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - q^{11} + 6q^{13} - q^{15} - 2q^{17} + O(q^{20})$$

## 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.