# Properties

 Label 38025bc Number of curves 8 Conductor 38025 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("38025.cj1")

sage: E.isogeny_class()

## Elliptic curves in class 38025bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38025.cj7 38025bc1 [1, -1, 0, -792, -1381509] [2] 110592 $$\Gamma_0(N)$$-optimal
38025.cj6 38025bc2 [1, -1, 0, -190917, -31611384] [2, 2] 221184
38025.cj5 38025bc3 [1, -1, 0, -381042, 41966991] [2, 2] 442368
38025.cj4 38025bc4 [1, -1, 0, -3042792, -2042183259] [2] 442368
38025.cj8 38025bc5 [1, -1, 0, 1330083, 314035866] [2] 884736
38025.cj2 38025bc6 [1, -1, 0, -5134167, 4476632616] [2, 2] 884736
38025.cj3 38025bc7 [1, -1, 0, -4183542, 6184905741] [2] 1769472
38025.cj1 38025bc8 [1, -1, 0, -82134792, 286529921991] [2] 1769472

## Rank

sage: E.rank()

The elliptic curves in class 38025bc have rank $$0$$.

## Modular form 38025.2.a.cj

sage: E.q_eigenform(10)

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

## 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.