# Properties

 Label 246.a Number of curves 2 Conductor 246 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("246.a1")

sage: E.isogeny_class()

## Elliptic curves in class 246.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
246.a1 246d1 [1, 1, 0, -66, 180] [2] 48 $$\Gamma_0(N)$$-optimal
246.a2 246d2 [1, 1, 0, -26, 444] [2] 96

## Rank

sage: E.rank()

The elliptic curves in class 246.a have rank $$1$$.

## Modular form246.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + 2q^{10} - 4q^{11} - q^{12} - 4q^{13} - 2q^{14} + 2q^{15} + q^{16} - 2q^{17} - q^{18} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.