# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 27930.dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
27930.dm1 27930dn4 $$[1, 0, 0, -30430, 2037650]$$ $$26487576322129/44531250$$ $$5239057031250$$ $$[2]$$ $$98304$$ $$1.3359$$
27930.dm2 27930dn2 $$[1, 0, 0, -2500, 9932]$$ $$14688124849/8122500$$ $$955604002500$$ $$[2, 2]$$ $$49152$$ $$0.98930$$
27930.dm3 27930dn1 $$[1, 0, 0, -1520, -22800]$$ $$3301293169/22800$$ $$2682397200$$ $$[2]$$ $$24576$$ $$0.64272$$ $$\Gamma_0(N)$$-optimal
27930.dm4 27930dn3 $$[1, 0, 0, 9750, 80982]$$ $$871257511151/527800050$$ $$-62095148082450$$ $$[2]$$ $$98304$$ $$1.3359$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 27930.dm do not have complex multiplication.

## 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 LMFDB 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 LMFDB labels.