Properties

 Label 23184.bk Number of curves $6$ Conductor $23184$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23184.bk1")

sage: E.isogeny_class()

Elliptic curves in class 23184.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23184.bk1 23184bi6 [0, 0, 0, -11395299, -14805815582] [2] 786432
23184.bk2 23184bi4 [0, 0, 0, -2550819, 1568035618] [2] 393216
23184.bk3 23184bi3 [0, 0, 0, -730659, -218720990] [2, 2] 393216
23184.bk4 23184bi2 [0, 0, 0, -166179, 22311970] [2, 2] 196608
23184.bk5 23184bi1 [0, 0, 0, 18141, 1926178] [2] 98304 $$\Gamma_0(N)$$-optimal
23184.bk6 23184bi5 [0, 0, 0, 902301, -1057735838] [2] 786432

Rank

sage: E.rank()

The elliptic curves in class 23184.bk have rank $$1$$.

Modular form 23184.2.a.bk

sage: E.q_eigenform(10)

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

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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.