Properties

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

Show commands: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

Elliptic curves in class 6930.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.be1 6930bf1 $$[1, -1, 1, -1517, 19541]$$ $$529278808969/88704000$$ $$64665216000$$ $$$$ $$7680$$ $$0.79544$$ $$\Gamma_0(N)$$-optimal
6930.be2 6930bf2 $$[1, -1, 1, 2803, 107669]$$ $$3342032927351/8893500000$$ $$-6483361500000$$ $$$$ $$15360$$ $$1.1420$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form6930.2.a.be

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} + q^{11} - q^{14} + q^{16} - 4 q^{17} + O(q^{20})$$ 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. 