# Properties

 Label 23104.bs Number of curves $3$ Conductor $23104$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

## Elliptic curves in class 23104.bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23104.bs1 23104bz3 $$[0, -1, 0, -1110917, -450312229]$$ $$-50357871050752/19$$ $$-57207791296$$ $$[]$$ $$155520$$ $$1.8522$$
23104.bs2 23104bz2 $$[0, -1, 0, -13477, -636189]$$ $$-89915392/6859$$ $$-20652012657856$$ $$[]$$ $$51840$$ $$1.3029$$
23104.bs3 23104bz1 $$[0, -1, 0, 963, -829]$$ $$32768/19$$ $$-57207791296$$ $$[]$$ $$17280$$ $$0.75362$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 23104.bs have rank $$1$$.

## Complex multiplication

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

## Modular form 23104.2.a.bs

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 LMFDB 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 LMFDB labels. 