Properties

 Label 46800.de Number of curves $6$ Conductor $46800$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46800.de1")

sage: E.isogeny_class()

Elliptic curves in class 46800.de

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46800.de1 46800cx6 [0, 0, 0, -32454075, -71162617750] [2] 2359296
46800.de2 46800cx4 [0, 0, 0, -3042075, 2040610250] [2] 1179648
46800.de3 46800cx3 [0, 0, 0, -2034075, -1105357750] [2, 2] 1179648
46800.de4 46800cx5 [0, 0, 0, -414075, -2817697750] [2] 2359296
46800.de5 46800cx2 [0, 0, 0, -234075, 16042250] [2, 2] 589824
46800.de6 46800cx1 [0, 0, 0, 53925, 1930250] [2] 294912 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 46800.de have rank $$1$$.

Modular form 46800.2.a.de

sage: E.q_eigenform(10)

$$q + 4q^{11} - q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.