# Properties

 Label 38808.p Number of curves 4 Conductor 38808 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38808.p1")

sage: E.isogeny_class()

## Elliptic curves in class 38808.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38808.p1 38808cn4 [0, 0, 0, -310611, 66630494]  221184
38808.p2 38808cn3 [0, 0, 0, -46011, -2345434]  221184
38808.p3 38808cn2 [0, 0, 0, -19551, 1025570] [2, 2] 110592
38808.p4 38808cn1 [0, 0, 0, 294, 53165]  55296 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 38808.p have rank $$1$$.

## Modular form 38808.2.a.p

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{11} - 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 