# Properties

 Label 37026.bk Number of curves 4 Conductor 37026 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37026.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 37026.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37026.bk1 37026ba4 [1, -1, 1, -123080, -11454055] [2] 311040
37026.bk2 37026ba3 [1, -1, 1, -112190, -14433559] [2] 155520
37026.bk3 37026ba2 [1, -1, 1, -46850, 3913913] [2] 103680
37026.bk4 37026ba1 [1, -1, 1, -3290, 45785] [2] 51840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 37026.bk have rank $$0$$.

## Modular form 37026.2.a.bk

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.