# Properties

 Label 158400fc Number of curves $4$ Conductor $158400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fc1")

sage: E.isogeny_class()

## Elliptic curves in class 158400fc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
158400.ku4 158400fc1 $$[0, 0, 0, 196800, -123469000]$$ $$72268906496/606436875$$ $$-7073479710000000000$$ $$[2]$$ $$1769472$$ $$2.2983$$ $$\Gamma_0(N)$$-optimal
158400.ku3 158400fc2 $$[0, 0, 0, -2840700, -1696894000]$$ $$13584145739344/1195803675$$ $$223165665043200000000$$ $$[2]$$ $$3538944$$ $$2.6448$$
158400.ku2 158400fc3 $$[0, 0, 0, -14059200, -20306401000]$$ $$-26348629355659264/24169921875$$ $$-281917968750000000000$$ $$[2]$$ $$5308416$$ $$2.8476$$
158400.ku1 158400fc4 $$[0, 0, 0, -224996700, -1299009526000]$$ $$6749703004355978704/5671875$$ $$1058508000000000000$$ $$[2]$$ $$10616832$$ $$3.1942$$

## Rank

sage: E.rank()

The elliptic curves in class 158400fc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 158400fc do not have complex multiplication.

## Modular form 158400.2.a.fc

sage: E.q_eigenform(10)

$$q + 2q^{7} - q^{11} + 2q^{13} + 2q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.