# Properties

 Label 141120.mc Number of curves $8$ Conductor $141120$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.mc1")

sage: E.isogeny_class()

## Elliptic curves in class 141120.mc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.mc1 141120jf7 [0, 0, 0, -182073612, 594925855216] [2] 42467328
141120.mc2 141120jf4 [0, 0, 0, -162599052, 798040774384] [2] 14155776
141120.mc3 141120jf6 [0, 0, 0, -76233612, -249380992784] [2, 2] 21233664
141120.mc4 141120jf3 [0, 0, 0, -75669132, -253352899856] [2] 10616832
141120.mc5 141120jf2 [0, 0, 0, -10189452, 12399768304] [2, 2] 7077888
141120.mc6 141120jf5 [0, 0, 0, -2286732, 31141859056] [2] 14155776
141120.mc7 141120jf1 [0, 0, 0, -1157772, -168717584] [2] 3538944 $$\Gamma_0(N)$$-optimal
141120.mc8 141120jf8 [0, 0, 0, 20574708, -839485788176] [2] 42467328

## Rank

sage: E.rank()

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

## Modular form 141120.2.a.mc

sage: E.q_eigenform(10)

$$q + q^{5} + 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.