Properties

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

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("lu1")

sage: E.isogeny_class()

Elliptic curves in class 187200lu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.fi2 187200lu1 $$[0, 0, 0, 57300, 14654000]$$ $$6967871/35100$$ $$-104808038400000000$$ $$[2]$$ $$1769472$$ $$1.9481$$ $$\Gamma_0(N)$$-optimal
187200.fi1 187200lu2 $$[0, 0, 0, -662700, 186014000]$$ $$10779215329/1232010$$ $$3678762147840000000$$ $$[2]$$ $$3538944$$ $$2.2947$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 187200.2.a.lu

sage: E.q_eigenform(10)

$$q - 2q^{7} + 4q^{11} - q^{13} + 8q^{17} + 6q^{19} + O(q^{20})$$

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 Cremona 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 Cremona labels.