# Properties

 Label 106470fe Number of curves 8 Conductor 106470 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("106470.fd1")

sage: E.isogeny_class()

## Elliptic curves in class 106470fe

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
106470.fd7 106470fe1 [1, -1, 1, -39127757, -93690555019] [2] 12386304 $$\Gamma_0(N)$$-optimal
106470.fd6 106470fe2 [1, -1, 1, -62977037, 34036648949] [2, 2] 24772608
106470.fd5 106470fe3 [1, -1, 1, -241724957, 1383584710421] [2] 37158912
106470.fd8 106470fe4 [1, -1, 1, 247489483, 269867017541] [2] 49545216
106470.fd4 106470fe5 [1, -1, 1, -755032037, 7972461142949] [2] 49545216
106470.fd2 106470fe6 [1, -1, 1, -3820607537, 90897164248349] [2, 2] 74317824
106470.fd3 106470fe7 [1, -1, 1, -3773654267, 93240113640041] [2] 148635648
106470.fd1 106470fe8 [1, -1, 1, -61129682087, 5817380358693089] [2] 148635648

## Rank

sage: E.rank()

The elliptic curves in class 106470fe have rank $$0$$.

## Modular form 106470.2.a.fd

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - q^{14} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.