# Properties

 Label 3528i Number of curves $2$ Conductor $3528$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 3528i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3528.m2 3528i1 [0, 0, 0, 105, -1078] [2] 1024 $$\Gamma_0(N)$$-optimal
3528.m1 3528i2 [0, 0, 0, -1155, -13426] [2] 2048

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3528.2.a.i

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.