# Properties

 Label 40310.p Number of curves 2 Conductor 40310 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40310.p1")

sage: E.isogeny_class()

## Elliptic curves in class 40310.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40310.p1 40310bd2 [1, -1, 1, -310196027862, -66496985128639551] [] 206524416
40310.p2 40310bd1 [1, -1, 1, -99013362, -835939931151]  29503488 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 40310.p have rank $$0$$.

## Modular form 40310.2.a.p

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 