Properties

 Label 176400fx Number of curves $2$ Conductor $176400$ CM no Rank $2$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("176400.nw1")

sage: E.isogeny_class()

Elliptic curves in class 176400fx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.nw1 176400fx1 [0, 0, 0, -54075, -1849750] [2] 884736 $$\Gamma_0(N)$$-optimal
176400.nw2 176400fx2 [0, 0, 0, 197925, -14197750] [2] 1769472

Rank

sage: E.rank()

The elliptic curves in class 176400fx have rank $$2$$.

Modular form 176400.2.a.nw

sage: E.q_eigenform(10)

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

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.