Properties

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

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 91035.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.q1 91035bi4 $$[1, -1, 1, -292667, 61009566]$$ $$157551496201/13125$$ $$230951277388125$$ $$[2]$$ $$655360$$ $$1.8000$$
91035.q2 91035bi2 $$[1, -1, 1, -19562, 817224]$$ $$47045881/11025$$ $$193999073006025$$ $$[2, 2]$$ $$327680$$ $$1.4534$$
91035.q3 91035bi1 $$[1, -1, 1, -6557, -191964]$$ $$1771561/105$$ $$1847610219105$$ $$[2]$$ $$163840$$ $$1.1068$$ $$\Gamma_0(N)$$-optimal
91035.q4 91035bi3 $$[1, -1, 1, 45463, 5056854]$$ $$590589719/972405$$ $$-17110718239131405$$ $$[2]$$ $$655360$$ $$1.8000$$

Rank

sage: E.rank()

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

Complex multiplication

The elliptic curves in class 91035.q do not have complex multiplication.

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.