# Properties

 Label 110946.g Number of curves 4 Conductor 110946 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("110946.g1")

sage: E.isogeny_class()

## Elliptic curves in class 110946.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110946.g1 110946h3 [1, 1, 0, -135355, -19150307]  829440
110946.g2 110946h4 [1, 1, 0, -68115, -38098539]  1658880
110946.g3 110946h1 [1, 1, 0, -9280, 320716]  276480 $$\Gamma_0(N)$$-optimal
110946.g4 110946h2 [1, 1, 0, 7530, 1373022]  552960

## Rank

sage: E.rank()

The elliptic curves in class 110946.g have rank $$0$$.

## Modular form 110946.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - 2q^{7} - q^{8} + q^{9} + q^{11} - q^{12} + 4q^{13} + 2q^{14} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 