# Properties

 Label 91035.q Number of curves 4 Conductor 91035 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("91035.q1")

sage: E.isogeny_class()

## Elliptic curves in class 91035.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91035.q1 91035bi4 [1, -1, 1, -292667, 61009566] [2] 655360
91035.q2 91035bi2 [1, -1, 1, -19562, 817224] [2, 2] 327680
91035.q3 91035bi1 [1, -1, 1, -6557, -191964] [2] 163840 $$\Gamma_0(N)$$-optimal
91035.q4 91035bi3 [1, -1, 1, 45463, 5056854] [2] 655360

## Rank

sage: E.rank()

The elliptic curves in class 91035.q have rank $$1$$.

## Modular form 91035.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + q^{5} - q^{7} + 3q^{8} - q^{10} - 6q^{13} + q^{14} - q^{16} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.