# Properties

 Label 38291.d Number of curves 3 Conductor 38291 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38291.d1")

sage: E.isogeny_class()

## Elliptic curves in class 38291.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38291.d1 38291c3 [0, -1, 1, -27222580, 54678189475] [] 1036750
38291.d2 38291c2 [0, -1, 1, -35970, 4768035] [] 207350
38291.d3 38291c1 [0, -1, 1, -1160, -35745] [] 41470 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 38291.d have rank $$0$$.

## Modular form 38291.2.a.d

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 