# Properties

 Label 18928z Number of curves 6 Conductor 18928 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("18928.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 18928z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18928.bb5 18928z1 [0, -1, 0, -1408, -40704] [2] 17280 $$\Gamma_0(N)$$-optimal
18928.bb4 18928z2 [0, -1, 0, -28448, -1836160] [2] 34560
18928.bb6 18928z3 [0, -1, 0, 12112, 857024] [2] 51840
18928.bb3 18928z4 [0, -1, 0, -96048, 9423296] [2] 103680
18928.bb2 18928z5 [0, -1, 0, -461088, 121011968] [2] 155520
18928.bb1 18928z6 [0, -1, 0, -7383328, 7724400384] [2] 311040

## Rank

sage: E.rank()

The elliptic curves in class 18928z have rank $$1$$.

## Modular form 18928.2.a.bb

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{7} + q^{9} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.