Properties

 Label 53550dx Number of curves $4$ Conductor $53550$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dx1")

sage: E.isogeny_class()

Elliptic curves in class 53550dx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53550.ec4 53550dx1 $$[1, -1, 1, 220, -340153]$$ $$103823/4386816$$ $$-49968576000000$$ $$[2]$$ $$196608$$ $$1.3074$$ $$\Gamma_0(N)$$-optimal
53550.ec3 53550dx2 $$[1, -1, 1, -71780, -7252153]$$ $$3590714269297/73410624$$ $$836192889000000$$ $$[2, 2]$$ $$393216$$ $$1.6540$$
53550.ec2 53550dx3 $$[1, -1, 1, -152780, 12187847]$$ $$34623662831857/14438442312$$ $$164462881960125000$$ $$[2]$$ $$786432$$ $$2.0006$$
53550.ec1 53550dx4 $$[1, -1, 1, -1142780, -469924153]$$ $$14489843500598257/6246072$$ $$71146663875000$$ $$[2]$$ $$786432$$ $$2.0006$$

Rank

sage: E.rank()

The elliptic curves in class 53550dx have rank $$1$$.

Complex multiplication

The elliptic curves in class 53550dx do not have complex multiplication.

Modular form 53550.2.a.dx

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{7} + q^{8} + 6q^{13} + q^{14} + q^{16} + q^{17} + O(q^{20})$$

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 Cremona 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 Cremona labels.