# Properties

 Label 3528.d Number of curves $6$ Conductor $3528$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 3528.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.d1 3528l5 [0, 0, 0, -169491, -26857586] [2] 12288
3528.d2 3528l4 [0, 0, 0, -28371, 1839166] [2] 6144
3528.d3 3528l3 [0, 0, 0, -10731, -408170] [2, 2] 6144
3528.d4 3528l2 [0, 0, 0, -1911, 24010] [2, 2] 3072
3528.d5 3528l1 [0, 0, 0, 294, 2401] [2] 1536 $$\Gamma_0(N)$$-optimal
3528.d6 3528l6 [0, 0, 0, 6909, -1618274] [2] 12288

## Rank

sage: E.rank()

The elliptic curves in class 3528.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3528.d do not have complex multiplication.

## Modular form3528.2.a.d

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.