# Properties

 Label 27930.ca Number of curves $4$ Conductor $27930$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("27930.ca1")

sage: E.isogeny_class()

## Elliptic curves in class 27930.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27930.ca1 27930ch4 [1, 1, 1, -148961, -22190827]  110592
27930.ca2 27930ch3 [1, 1, 1, -10781, -233731]  110592
27930.ca3 27930ch2 [1, 1, 1, -9311, -349567] [2, 2] 55296
27930.ca4 27930ch1 [1, 1, 1, -491, -7351]  27648 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 27930.2.a.ca

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 