Properties

 Label 308550.fy Number of curves $2$ Conductor $308550$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fy1")

sage: E.isogeny_class()

Elliptic curves in class 308550.fy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
308550.fy1 308550fy2 [1, 1, 1, -550613, -157481719] [2] 2949120
308550.fy2 308550fy1 [1, 1, 1, -36363, -2178219] [2] 1474560 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 308550.fy have rank $$0$$.

Complex multiplication

The elliptic curves in class 308550.fy do not have complex multiplication.

Modular form 308550.2.a.fy

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} - q^{12} + 4q^{13} - 2q^{14} + q^{16} + q^{17} + q^{18} - 2q^{19} + O(q^{20})$$

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.