Properties

 Label 28224.eo Number of curves $2$ Conductor $28224$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("eo1")

sage: E.isogeny_class()

Elliptic curves in class 28224.eo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28224.eo1 28224o1 $$[0, 0, 0, -10584, 370440]$$ $$55296/7$$ $$16598831993856$$ $$[2]$$ $$73728$$ $$1.2659$$ $$\Gamma_0(N)$$-optimal
28224.eo2 28224o2 $$[0, 0, 0, 15876, 1926288]$$ $$11664/49$$ $$-1859069183311872$$ $$[2]$$ $$147456$$ $$1.6125$$

Rank

sage: E.rank()

The elliptic curves in class 28224.eo have rank $$0$$.

Complex multiplication

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

Modular form 28224.2.a.eo

sage: E.q_eigenform(10)

$$q + 2q^{5} - 6q^{11} - 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.