# Properties

 Label 162450.d Number of curves $4$ Conductor $162450$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162450.d1")

sage: E.isogeny_class()

## Elliptic curves in class 162450.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162450.d1 162450dd3 [1, -1, 0, -246925692, 1493535273966]  26542080
162450.d2 162450dd4 [1, -1, 0, -17871192, 15475826466]  26542080
162450.d3 162450dd2 [1, -1, 0, -15434442, 23334345216] [2, 2] 13271040
162450.d4 162450dd1 [1, -1, 0, -813942, 482503716]  6635520 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 162450.d have rank $$1$$.

## Modular form 162450.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 4q^{7} - q^{8} + 4q^{11} - 2q^{13} + 4q^{14} + q^{16} - 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 