Properties

 Label 6720bf Number of curves 2 Conductor 6720 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.d1")

sage: E.isogeny_class()

Elliptic curves in class 6720bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.d1 6720bf1 [0, -1, 0, -2261, -40635] [2] 3840 $$\Gamma_0(N)$$-optimal
6720.d2 6720bf2 [0, -1, 0, -2161, -44495] [2] 7680

Rank

sage: E.rank()

The elliptic curves in class 6720bf have rank $$0$$.

Modular form6720.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 2q^{11} - 4q^{13} + q^{15} + 2q^{17} + 2q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.