# Properties

 Label 37905.g Number of curves 4 Conductor 37905 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37905.g1")

sage: E.isogeny_class()

## Elliptic curves in class 37905.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37905.g1 37905k4 [1, 1, 1, -40620, 3133920]  96768
37905.g2 37905k2 [1, 1, 1, -2715, 40872] [2, 2] 48384
37905.g3 37905k1 [1, 1, 1, -910, -10390]  24192 $$\Gamma_0(N)$$-optimal
37905.g4 37905k3 [1, 1, 1, 6310, 264692]  96768

## Rank

sage: E.rank()

The elliptic curves in class 37905.g have rank $$0$$.

## Modular form 37905.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 