# Properties

 Label 436425cd Number of curves 2 Conductor 436425 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("436425.cd1")

sage: E.isogeny_class()

## Elliptic curves in class 436425cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
436425.cd2 436425cd1 [1, 0, 1, -304451, 940225673]  12165120 $$\Gamma_0(N)$$-optimal*
436425.cd1 436425cd2 [1, 0, 1, -16372826, 25299882173]  24330240 $$\Gamma_0(N)$$-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 436425cd1.

## Rank

sage: E.rank()

The elliptic curves in class 436425cd have rank $$1$$.

## Modular form 436425.2.a.cd

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 