# Properties

 Label 58800.cu Number of curves 8 Conductor 58800 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58800.cu1")

sage: E.isogeny_class()

## Elliptic curves in class 58800.cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.cu1 58800fc7 [0, -1, 0, -104537008, -411354663488] [2] 3981312
58800.cu2 58800fc8 [0, -1, 0, -8889008, -1385383488] [2] 3981312
58800.cu3 58800fc6 [0, -1, 0, -6537008, -6418663488] [2, 2] 1990656
58800.cu4 58800fc5 [0, -1, 0, -5655008, 5177872512] [2] 1327104
58800.cu5 58800fc4 [0, -1, 0, -1343008, -515535488] [2] 1327104
58800.cu6 58800fc2 [0, -1, 0, -363008, 76384512] [2, 2] 663552
58800.cu7 58800fc3 [0, -1, 0, -265008, -171751488] [2] 995328
58800.cu8 58800fc1 [0, -1, 0, 28992, 5824512] [2] 331776 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 58800.cu have rank $$1$$.

## Modular form 58800.2.a.cu

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.