Properties

 Label 100016e Number of curves 2 Conductor 100016 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100016.b1")
sage: E.isogeny_class()

Elliptic curves in class 100016e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100016.b2 100016e1 [0, 1, 0, -242247, -45976760] 2 584064 $$\Gamma_0(N)$$-optimal
100016.b1 100016e2 [0, 1, 0, -3876052, -2938485540] 2 1168128

Rank

sage: E.rank()

The elliptic curves in class 100016e have rank $$0$$.

Modular form 100016.2.a.b

sage: E.q_eigenform(10)
$$q - 2q^{3} + 2q^{5} + q^{7} + q^{9} - 2q^{13} - 4q^{15} - 2q^{17} - q^{19} + O(q^{20})$$

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. 