Properties

 Label 22050.cz Number of curves $2$ Conductor $22050$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cz1")

sage: E.isogeny_class()

Elliptic curves in class 22050.cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
22050.cz1 22050fu2 $$[1, -1, 1, -154580, -24711753]$$ $$-7620530425/526848$$ $$-28241068322880000$$ $$[]$$ $$248832$$ $$1.9076$$
22050.cz2 22050fu1 $$[1, -1, 1, 10795, -37803]$$ $$2595575/1512$$ $$-81048984345000$$ $$[]$$ $$82944$$ $$1.3583$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 22050.cz have rank $$1$$.

Complex multiplication

The elliptic curves in class 22050.cz do not have complex multiplication.

Modular form 22050.2.a.cz

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 6q^{11} + q^{13} + q^{16} + 3q^{17} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.