# Properties

 Label 38976bb Number of curves $6$ Conductor $38976$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("38976.t1")

sage: E.isogeny_class()

## Elliptic curves in class 38976bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38976.t5 38976bb1 [0, -1, 0, -50177, -4615263] [2] 196608 $$\Gamma_0(N)$$-optimal
38976.t4 38976bb2 [0, -1, 0, -818497, -284744735] [2, 2] 393216
38976.t3 38976bb3 [0, -1, 0, -834177, -273251295] [2, 2] 786432
38976.t1 38976bb4 [0, -1, 0, -13095937, -18236817503] [2] 786432
38976.t6 38976bb5 [0, -1, 0, 798783, -1214162847] [2] 1572864
38976.t2 38976bb6 [0, -1, 0, -2718017, 1402989537] [2] 1572864

## Rank

sage: E.rank()

The elliptic curves in class 38976bb have rank $$0$$.

## Modular form 38976.2.a.t

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - q^{7} + q^{9} + 4q^{11} + 2q^{13} - 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.