# Properties

 Label 35520v Number of curves $6$ Conductor $35520$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35520.bw1")

sage: E.isogeny_class()

## Elliptic curves in class 35520v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35520.bw5 35520v1 [0, 1, 0, -54081, 16646175] [2] 331776 $$\Gamma_0(N)$$-optimal
35520.bw4 35520v2 [0, 1, 0, -1364801, 611975199] [2, 2] 663552
35520.bw3 35520v3 [0, 1, 0, -1876801, 110522399] [2, 2] 1327104
35520.bw1 35520v4 [0, 1, 0, -21824321, 39235457055] [2] 1327104
35520.bw6 35520v5 [0, 1, 0, 7454399, 888744479] [2] 2654208
35520.bw2 35520v6 [0, 1, 0, -19400001, -32752486881] [2] 2654208

## Rank

sage: E.rank()

The elliptic curves in class 35520v have rank $$0$$.

## Modular form 35520.2.a.bw

sage: E.q_eigenform(10)

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

## 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.