# Properties

 Label 37026bj Number of curves 6 Conductor 37026 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37026.bm1")

sage: E.isogeny_class()

## Elliptic curves in class 37026bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37026.bm5 37026bj1 [1, -1, 1, -37049, 2554841] [2] 163840 $$\Gamma_0(N)$$-optimal
37026.bm4 37026bj2 [1, -1, 1, -124169, -13858567] [2, 2] 327680
37026.bm6 37026bj3 [1, -1, 1, 246091, -80949679] [2] 655360
37026.bm2 37026bj4 [1, -1, 1, -1888349, -998271007] [2, 2] 655360
37026.bm3 37026bj5 [1, -1, 1, -1790339, -1106591659] [2] 1310720
37026.bm1 37026bj6 [1, -1, 1, -30213239, -63913516675] [2] 1310720

## Rank

sage: E.rank()

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

## Modular form 37026.2.a.bm

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.