# Properties

 Label 26950.d Number of curves 4 Conductor 26950 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("26950.d1")

sage: E.isogeny_class()

## Elliptic curves in class 26950.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26950.d1 26950p4 [1, 0, 1, -31992126, 67672420148]  3981312
26950.d2 26950p2 [1, 0, 1, -4380626, -3498021852]  1327104
26950.d3 26950p1 [1, 0, 1, -68626, -134661852]  663552 $$\Gamma_0(N)$$-optimal
26950.d4 26950p3 [1, 0, 1, 617374, 3627362148]  1990656

## Rank

sage: E.rank()

The elliptic curves in class 26950.d have rank $$0$$.

## Modular form 26950.2.a.d

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 