# Properties

 Label 33810q Number of curves $2$ Conductor $33810$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 33810q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.r1 33810q1 $$[1, 1, 0, -1152, -8784]$$ $$1439069689/579600$$ $$68189360400$$ $$$$ $$36864$$ $$0.77676$$ $$\Gamma_0(N)$$-optimal
33810.r2 33810q2 $$[1, 1, 0, 3748, -58764]$$ $$49471280711/41992020$$ $$-4940319160980$$ $$$$ $$73728$$ $$1.1233$$

## Rank

sage: E.rank()

The elliptic curves in class 33810q have rank $$1$$.

## Complex multiplication

The elliptic curves in class 33810q do not have complex multiplication.

## Modular form 33810.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} - 2q^{11} - q^{12} - 4q^{13} - q^{15} + q^{16} + 6q^{17} - q^{18} + 4q^{19} + O(q^{20})$$ ## 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. 