Properties

 Label 6930.j Number of curves $2$ Conductor $6930$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

Elliptic curves in class 6930.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.j1 6930l1 $$[1, -1, 0, -54, 0]$$ $$24137569/13860$$ $$10103940$$ $$$$ $$1536$$ $$0.033680$$ $$\Gamma_0(N)$$-optimal
6930.j2 6930l2 $$[1, -1, 0, 216, -162]$$ $$1524845951/889350$$ $$-648336150$$ $$$$ $$3072$$ $$0.38025$$

Rank

sage: E.rank()

The elliptic curves in class 6930.j have rank $$1$$.

Complex multiplication

The elliptic curves in class 6930.j do not have complex multiplication.

Modular form6930.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{7} - q^{8} - q^{10} - q^{11} + 4 q^{13} + q^{14} + q^{16} - 4 q^{19} + O(q^{20})$$ 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 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. 