# Properties

 Label 26775x Number of curves 4 Conductor 26775 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("26775.n1")

sage: E.isogeny_class()

## Elliptic curves in class 26775x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26775.n4 26775x1 [1, -1, 1, 3145, -114978]  49152 $$\Gamma_0(N)$$-optimal
26775.n3 26775x2 [1, -1, 1, -24980, -1239978] [2, 2] 98304
26775.n2 26775x3 [1, -1, 1, -120605, 15016272]  196608
26775.n1 26775x4 [1, -1, 1, -379355, -89833728]  196608

## Rank

sage: E.rank()

The elliptic curves in class 26775x have rank $$0$$.

## Modular form 26775.2.a.n

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - q^{7} + 3q^{8} + 6q^{13} + q^{14} - q^{16} - q^{17} + 4q^{19} + O(q^{20})$$

## 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. 