Properties

 Label 28224.co Number of curves $2$ Conductor $28224$ CM no Rank $1$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

Elliptic curves in class 28224.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.co1 28224bs2 $$[0, 0, 0, -81228, -9244816]$$ $$-6329617441/279936$$ $$-2621333531787264$$ $$[]$$ $$129024$$ $$1.7235$$
28224.co2 28224bs1 $$[0, 0, 0, -588, 12656]$$ $$-2401/6$$ $$-56184274944$$ $$[]$$ $$18432$$ $$0.75055$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 28224.co have rank $$1$$.

Complex multiplication

The elliptic curves in class 28224.co do not have complex multiplication.

Modular form 28224.2.a.co

sage: E.q_eigenform(10)

$$q - q^{5} + 5q^{11} - 4q^{17} + 8q^{19} + O(q^{20})$$

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.