# Properties

 Label 32370bg Number of curves 2 Conductor 32370 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("32370.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 32370bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32370.bj2 32370bg1 [1, 0, 0, -286625, 137015625]  812224 $$\Gamma_0(N)$$-optimal
32370.bj1 32370bg2 [1, 0, 0, -39869525, -100494513555] [] 5685568

## Rank

sage: E.rank()

The elliptic curves in class 32370bg have rank $$0$$.

## Modular form 32370.2.a.bj

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2q^{11} + q^{12} - q^{13} + q^{14} + q^{15} + q^{16} + 4q^{17} + q^{18} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 