# Properties

 Label 350d Number of curves 6 Conductor 350 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("350.f1")

sage: E.isogeny_class()

## Elliptic curves in class 350d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
350.f5 350d1 [1, 1, 1, -13, 31] [2] 48 $$\Gamma_0(N)$$-optimal
350.f4 350d2 [1, 1, 1, -263, 1531] [2] 96
350.f6 350d3 [1, 1, 1, 112, -719] [2] 144
350.f3 350d4 [1, 1, 1, -888, -8719] [2] 288
350.f2 350d5 [1, 1, 1, -4263, -109219] [2] 432
350.f1 350d6 [1, 1, 1, -68263, -6893219] [2] 864

## Rank

sage: E.rank()

The elliptic curves in class 350d have rank $$0$$.

## Modular form350.2.a.f

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.