# Properties

 Label 141120.eg Number of curves 8 Conductor 141120 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("141120.eg1")

sage: E.isogeny_class()

## Elliptic curves in class 141120.eg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
141120.eg1 141120lz8 [0, 0, 0, -9913186668, -379898903267408] [2] 84934656
141120.eg2 141120lz6 [0, 0, 0, -619587948, -5935643093072] [2, 2] 42467328
141120.eg3 141120lz7 [0, 0, 0, -574429548, -6837564721232] [2] 84934656
141120.eg4 141120lz5 [0, 0, 0, -122986668, -515740787408] [2] 28311552
141120.eg5 141120lz3 [0, 0, 0, -41560428, -78374627408] [2] 21233664
141120.eg6 141120lz2 [0, 0, 0, -16299948, 13297319728] [2, 2] 14155776
141120.eg7 141120lz1 [0, 0, 0, -14042028, 20245391152] [2] 7077888 $$\Gamma_0(N)$$-optimal
141120.eg8 141120lz4 [0, 0, 0, 54260052, 97658855728] [2] 28311552

## Rank

sage: E.rank()

The elliptic curves in class 141120.eg have rank $$1$$.

## Modular form 141120.2.a.eg

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.