# Properties

 Label 30446f Number of curves 3 Conductor 30446 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("30446.a1")

sage: E.isogeny_class()

## Elliptic curves in class 30446f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30446.a2 30446f1 [1, 0, 1, -35601, 2916644] [3] 111456 $$\Gamma_0(N)$$-optimal
30446.a3 30446f2 [1, 0, 1, 239024, -10823394] [3] 334368
30446.a1 30446f3 [1, 0, 1, -3795071, -2955377838] [] 1003104

## Rank

sage: E.rank()

The elliptic curves in class 30446f have rank $$1$$.

## Modular form 30446.2.a.a

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.