# Properties

 Label 38.a Number of curves 3 Conductor 38 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38.a1")

sage: E.isogeny_class()

## Elliptic curves in class 38.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38.a1 38a2 [1, 0, 1, -86, -2456] [] 18
38.a2 38a3 [1, 0, 1, -16, 22]  18
38.a3 38a1 [1, 0, 1, 9, 90]  6 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 38.a have rank $$0$$.

## Modular form38.2.a.a

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 