Properties

 Label 6930n Number of curves 4 Conductor 6930 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.l1")
sage: E.isogeny_class()

Elliptic curves in class 6930n

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.l3 6930n1 [1, -1, 0, -8919, 225693] 2 20480 $$\Gamma_0(N)$$-optimal
6930.l2 6930n2 [1, -1, 0, -54999, -4778595] 4 40960
6930.l1 6930n3 [1, -1, 0, -871479, -312918147] 2 81920
6930.l4 6930n4 [1, -1, 0, 24201, -17466435] 2 81920

Rank

sage: E.rank()

The elliptic curves in class 6930n have rank $$0$$.

Modular form6930.2.a.l

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} + q^{11} - 6q^{13} + q^{14} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

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 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.