# Properties

 Label 277200lk Number of curves $4$ Conductor $277200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("lk1")

sage: E.isogeny_class()

## Elliptic curves in class 277200lk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277200.lk4 277200lk1 $$[0, 0, 0, -422830875, -3346556093750]$$ $$1433528304665250149/162339408$$ $$946763427456000000000$$ $$[2]$$ $$36864000$$ $$3.4489$$ $$\Gamma_0(N)$$-optimal
277200.lk3 277200lk2 $$[0, 0, 0, -423910875, -3328601093750]$$ $$1444540994277943589/15251205665388$$ $$88945031440542816000000000$$ $$[2]$$ $$73728000$$ $$3.7955$$
277200.lk2 277200lk3 $$[0, 0, 0, -1562320875, 20258583156250]$$ $$72313087342699809269/11447096545640448$$ $$66759467054175092736000000000$$ $$[2]$$ $$184320000$$ $$4.2536$$
277200.lk1 277200lk4 $$[0, 0, 0, -23957200875, 1427216919156250]$$ $$260744057755293612689909/8504954620259328$$ $$49600895345352400896000000000$$ $$[2]$$ $$368640000$$ $$4.6002$$

## Rank

sage: E.rank()

The elliptic curves in class 277200lk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 277200lk do not have complex multiplication.

## Modular form 277200.2.a.lk

sage: E.q_eigenform(10)

$$q + q^{7} + q^{11} - 4 q^{13} - 2 q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.