# Properties

 Label 35490ct Number of curves $4$ Conductor $35490$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 35490ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35490.cw3 35490ct1 [1, 1, 1, -595, -3775]  36864 $$\Gamma_0(N)$$-optimal
35490.cw2 35490ct2 [1, 1, 1, -3975, 92217] [2, 2] 73728
35490.cw4 35490ct3 [1, 1, 1, 1095, 317325]  147456
35490.cw1 35490ct4 [1, 1, 1, -63125, 6078197]  147456

## Rank

sage: E.rank()

The elliptic curves in class 35490ct have rank $$0$$.

## Complex multiplication

The elliptic curves in class 35490ct do not have complex multiplication.

## Modular form 35490.2.a.ct

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} + q^{14} - q^{15} + q^{16} - 6q^{17} + q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 