Properties

 Label 6930.bb Number of curves $4$ Conductor $6930$ CM no Rank $0$ Graph

Related objects

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

Elliptic curves in class 6930.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bb1 6930bd3 $$[1, -1, 1, -234392, -43615969]$$ $$1953542217204454969/170843779260$$ $$124545115080540$$ $$[2]$$ $$40960$$ $$1.7459$$
6930.bb2 6930bd4 $$[1, -1, 1, -84992, 9070751]$$ $$93137706732176569/5369647977540$$ $$3914473375626660$$ $$[2]$$ $$40960$$ $$1.7459$$
6930.bb3 6930bd2 $$[1, -1, 1, -15692, -575809]$$ $$586145095611769/140040608400$$ $$102089603523600$$ $$[2, 2]$$ $$20480$$ $$1.3994$$
6930.bb4 6930bd1 $$[1, -1, 1, 2308, -57409]$$ $$1865864036231/2993760000$$ $$-2182451040000$$ $$[4]$$ $$10240$$ $$1.0528$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form6930.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - q^{7} + q^{8} + q^{10} - q^{11} - 2 q^{13} - q^{14} + q^{16} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.