Properties

 Label 6930.bi Number of curves $4$ Conductor $6930$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

Elliptic curves in class 6930.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bi1 6930bm3 $$[1, -1, 1, -7772, 263621]$$ $$71210194441849/631496250$$ $$460360766250$$ $$$$ $$16384$$ $$1.0612$$
6930.bi2 6930bm2 $$[1, -1, 1, -842, -2491]$$ $$90458382169/48024900$$ $$35010152100$$ $$[2, 2]$$ $$8192$$ $$0.71467$$
6930.bi3 6930bm1 $$[1, -1, 1, -662, -6379]$$ $$43949604889/55440$$ $$40415760$$ $$$$ $$4096$$ $$0.36810$$ $$\Gamma_0(N)$$-optimal
6930.bi4 6930bm4 $$[1, -1, 1, 3208, -21931]$$ $$5009866738631/3163773690$$ $$-2306391020010$$ $$$$ $$16384$$ $$1.0612$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form6930.2.a.bi

sage: E.q_eigenform(10)

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 