# Properties

 Label 27753.c Number of curves 4 Conductor 27753 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("27753.c1")

sage: E.isogeny_class()

## Elliptic curves in class 27753.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27753.c1 27753d4 [1, 0, 0, -123224, 16622493]  145152
27753.c2 27753d2 [1, 0, 0, -9689, 114504] [2, 2] 72576
27753.c3 27753d1 [1, 0, 0, -5484, -155457]  36288 $$\Gamma_0(N)$$-optimal
27753.c4 27753d3 [1, 0, 0, 36566, 900839]  145152

## Rank

sage: E.rank()

The elliptic curves in class 27753.c have rank $$0$$.

## Modular form 27753.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - 2q^{5} - q^{6} + 4q^{7} + 3q^{8} + q^{9} + 2q^{10} - q^{11} - q^{12} - 2q^{13} - 4q^{14} - 2q^{15} - q^{16} + 2q^{17} - q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 