# Properties

 Label 141120kc Number of curves $2$ Conductor $141120$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("kc1")

sage: E.isogeny_class()

## Elliptic curves in class 141120kc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.oy2 141120kc1 $$[0, 0, 0, 1428, -22736]$$ $$19652/25$$ $$-409677004800$$ $$[2]$$ $$147456$$ $$0.91420$$ $$\Gamma_0(N)$$-optimal
141120.oy1 141120kc2 $$[0, 0, 0, -8652, -220304]$$ $$2185454/625$$ $$20483850240000$$ $$[2]$$ $$294912$$ $$1.2608$$

## Rank

sage: E.rank()

The elliptic curves in class 141120kc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 141120kc do not have complex multiplication.

## Modular form 141120.2.a.kc

sage: E.q_eigenform(10)

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

## 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 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.