# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("da1")

sage: E.isogeny_class()

## Elliptic curves in class 33810da

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33810.cs1 33810da1 $$[1, 0, 0, -12006, -484380]$$ $$1626794704081/83462400$$ $$9819267897600$$ $$$$ $$147456$$ $$1.2508$$ $$\Gamma_0(N)$$-optimal
33810.cs2 33810da2 $$[1, 0, 0, 7594, -1907340]$$ $$411664745519/13605414480$$ $$-1600663408157520$$ $$$$ $$294912$$ $$1.5974$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 33810.2.a.da

sage: E.q_eigenform(10)

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