Properties

 Label 84150.co Number of curves $2$ Conductor $84150$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

Elliptic curves in class 84150.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84150.co1 84150bp2 [1, -1, 0, -32292, -1418634] [2] 393216
84150.co2 84150bp1 [1, -1, 0, 5958, -156384] [2] 196608 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 84150.co have rank $$1$$.

Complex multiplication

The elliptic curves in class 84150.co do not have complex multiplication.

Modular form 84150.2.a.co

sage: E.q_eigenform(10)

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

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 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.