# Properties

 Label 23104u Number of curves $3$ Conductor $23104$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 23104u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23104.i3 23104u1 $$[0, 1, 0, 963, 829]$$ $$32768/19$$ $$-57207791296$$ $$[]$$ $$17280$$ $$0.75362$$ $$\Gamma_0(N)$$-optimal
23104.i2 23104u2 $$[0, 1, 0, -13477, 636189]$$ $$-89915392/6859$$ $$-20652012657856$$ $$[]$$ $$51840$$ $$1.3029$$
23104.i1 23104u3 $$[0, 1, 0, -1110917, 450312229]$$ $$-50357871050752/19$$ $$-57207791296$$ $$[]$$ $$155520$$ $$1.8522$$

## Rank

sage: E.rank()

The elliptic curves in class 23104u have rank $$2$$.

## Complex multiplication

The elliptic curves in class 23104u do not have complex multiplication.

## Modular form 23104.2.a.u

sage: E.q_eigenform(10)

$$q - 2q^{3} - 3q^{5} - q^{7} + q^{9} - 3q^{11} - 4q^{13} + 6q^{15} - 3q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.