# Properties

 Label 27930dn Number of curves $4$ Conductor $27930$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("27930.dm1")

sage: E.isogeny_class()

## Elliptic curves in class 27930dn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27930.dm3 27930dn1 [1, 0, 0, -1520, -22800] [2] 24576 $$\Gamma_0(N)$$-optimal
27930.dm2 27930dn2 [1, 0, 0, -2500, 9932] [2, 2] 49152
27930.dm4 27930dn3 [1, 0, 0, 9750, 80982] [2] 98304
27930.dm1 27930dn4 [1, 0, 0, -30430, 2037650] [2] 98304

## Rank

sage: E.rank()

The elliptic curves in class 27930dn have rank $$0$$.

## Modular form 27930.2.a.dm

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.