# Properties

 Label 37026.z Number of curves $2$ Conductor $37026$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 37026.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37026.z1 37026bl2 [1, -1, 1, -198221, 34016051] [2] 184320
37026.z2 37026bl1 [1, -1, 1, -13091, 470495] [2] 92160 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 37026.z have rank $$1$$.

## Complex multiplication

The elliptic curves in class 37026.z do not have complex multiplication.

## Modular form 37026.2.a.z

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 2q^{5} + 2q^{7} + q^{8} - 2q^{10} - 4q^{13} + 2q^{14} + q^{16} + q^{17} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.