Properties

 Label 6720.i Number of curves 4 Conductor 6720 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6720.i1")

sage: E.isogeny_class()

Elliptic curves in class 6720.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6720.i1 6720d4 [0, -1, 0, -2721, 55521] [2] 4096
6720.i2 6720d3 [0, -1, 0, -1601, -23775] [2] 4096
6720.i3 6720d2 [0, -1, 0, -201, 585] [2, 2] 2048
6720.i4 6720d1 [0, -1, 0, 44, 46] [2] 1024 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 6720.i have rank $$1$$.

Modular form6720.2.a.i

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.