# Properties

 Label 95370.bp Number of curves $2$ Conductor $95370$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 95370.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
95370.bp1 95370bj2 [1, 0, 1, -41478, 2073406]  589824
95370.bp2 95370bj1 [1, 0, 1, 7652, 226118]  294912 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 95370.bp have rank $$1$$.

## Complex multiplication

The elliptic curves in class 95370.bp do not have complex multiplication.

## Modular form 95370.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} - q^{10} - q^{11} + q^{12} - 2q^{14} + q^{15} + q^{16} - q^{18} + O(q^{20})$$

## 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. 