# Properties

 Label 23805t Number of curves 8 Conductor 23805 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("23805.s1")

sage: E.isogeny_class()

## Elliptic curves in class 23805t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23805.s7 23805t1 [1, -1, 0, -99, 61240] [2] 25344 $$\Gamma_0(N)$$-optimal
23805.s6 23805t2 [1, -1, 0, -23904, 1408603] [2, 2] 50688
23805.s5 23805t3 [1, -1, 0, -47709, -1843160] [2, 2] 101376
23805.s4 23805t4 [1, -1, 0, -380979, 90605938] [2] 101376
23805.s8 23805t5 [1, -1, 0, 166536, -13969427] [2] 202752
23805.s2 23805t6 [1, -1, 0, -642834, -198115385] [2, 2] 202752
23805.s3 23805t7 [1, -1, 0, -523809, -273839090] [2] 405504
23805.s1 23805t8 [1, -1, 0, -10283859, -12690955580] [2] 405504

## Rank

sage: E.rank()

The elliptic curves in class 23805t have rank $$0$$.

## Modular form 23805.2.a.s

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.