# Properties

 Label 141120.gn Number of curves $4$ Conductor $141120$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gn1")

sage: E.isogeny_class()

## Elliptic curves in class 141120.gn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.gn1 141120ek4 $$[0, 0, 0, -180033840588, -29402166520305488]$$ $$229625675762164624948320008/9568125$$ $$26890107830046720000$$ $$[2]$$ $$330301440$$ $$4.6288$$
141120.gn2 141120ek2 $$[0, 0, 0, -11252115588, -459408804615488]$$ $$448487713888272974160064/91549016015625$$ $$32160989122670721600000000$$ $$[2, 2]$$ $$165150720$$ $$4.2822$$
141120.gn3 141120ek3 $$[0, 0, 0, -11213536908, -462715414141232]$$ $$-55486311952875723077768/801237030029296875$$ $$-2251783932057135000000000000000$$ $$[2]$$ $$330301440$$ $$4.6288$$
141120.gn4 141120ek1 $$[0, 0, 0, -705668943, -7126549533992]$$ $$7079962908642659949376/100085966990454375$$ $$549375049939540209358680000$$ $$[2]$$ $$82575360$$ $$3.9357$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 141120.2.a.gn

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.