# Properties

 Label 23184.ba Number of curves $2$ Conductor $23184$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 23184.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23184.ba1 23184bh2 $$[0, 0, 0, -87195, 9278026]$$ $$24553362849625/1755162752$$ $$5240887894867968$$ $$$$ $$129024$$ $$1.7632$$
23184.ba2 23184bh1 $$[0, 0, 0, 4965, 633418]$$ $$4533086375/60669952$$ $$-181159505952768$$ $$$$ $$64512$$ $$1.4166$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 23184.ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 23184.ba do not have complex multiplication.

## Modular form 23184.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{7} + 4q^{11} - 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 