Properties

 Label 37026.bp Number of curves $2$ Conductor $37026$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bp1")

sage: E.isogeny_class()

Elliptic curves in class 37026.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37026.bp1 37026bd1 [1, -1, 1, -984479, 373248263] [2] 1075200 $$\Gamma_0(N)$$-optimal
37026.bp2 37026bd2 [1, -1, 1, -287519, 890950151] [2] 2150400

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 37026.2.a.bp

sage: E.q_eigenform(10)

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

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.