Properties

 Label 187200.pt Number of curves $2$ Conductor $187200$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("pt1")

sage: E.isogeny_class()

Elliptic curves in class 187200.pt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.pt1 187200cc2 $$[0, 0, 0, -223500, -13250000]$$ $$26463592/13689$$ $$638673984000000000$$ $$[2]$$ $$2293760$$ $$2.1085$$
187200.pt2 187200cc1 $$[0, 0, 0, -178500, -29000000]$$ $$107850176/117$$ $$682344000000000$$ $$[2]$$ $$1146880$$ $$1.7620$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 187200.pt have rank $$0$$.

Complex multiplication

The elliptic curves in class 187200.pt do not have complex multiplication.

Modular form 187200.2.a.pt

sage: E.q_eigenform(10)

$$q + 4q^{7} + 2q^{11} - q^{13} + 2q^{19} + O(q^{20})$$

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.