Properties

 Label 24255.bn Number of curves $6$ Conductor $24255$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("24255.bn1")

sage: E.isogeny_class()

Elliptic curves in class 24255.bn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24255.bn1 24255bm6 [1, -1, 0, -5843259, -5434921962] [2] 786432
24255.bn2 24255bm4 [1, -1, 0, -385884, -74688237] [2, 2] 393216
24255.bn3 24255bm2 [1, -1, 0, -119079, 14798160] [2, 2] 196608
24255.bn4 24255bm1 [1, -1, 0, -116874, 15408063] [2] 98304 $$\Gamma_0(N)$$-optimal
24255.bn5 24255bm3 [1, -1, 0, 112446, 65224305] [2] 393216
24255.bn6 24255bm5 [1, -1, 0, 802611, -444785580] [2] 786432

Rank

sage: E.rank()

The elliptic curves in class 24255.bn have rank $$0$$.

Modular form 24255.2.a.bn

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + q^{5} - 3q^{8} + q^{10} - q^{11} + 2q^{13} - q^{16} - 6q^{17} + 4q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.