Properties

 Label 99450co Number of curves 4 Conductor 99450 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("99450.ce1")

sage: E.isogeny_class()

Elliptic curves in class 99450co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
99450.ce4 99450co1 [1, -1, 1, 355495, -13922503] [2] 2211840 $$\Gamma_0(N)$$-optimal
99450.ce3 99450co2 [1, -1, 1, -1444505, -111122503] [2, 2] 4423680
99450.ce2 99450co3 [1, -1, 1, -14449505, 21035007497] [2] 8847360
99450.ce1 99450co4 [1, -1, 1, -17239505, -27499652503] [2] 8847360

Rank

sage: E.rank()

The elliptic curves in class 99450co have rank $$1$$.

Modular form 99450.2.a.ce

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 4q^{7} + q^{8} + 4q^{11} - q^{13} - 4q^{14} + q^{16} - q^{17} + 8q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.