# Properties

 Label 23100.b Number of curves $4$ Conductor $23100$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 23100.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23100.b1 23100b4 $$[0, -1, 0, -1239908, 280602312]$$ $$52702650535889104/22020583921875$$ $$88082335687500000000$$ $$$$ $$746496$$ $$2.5241$$
23100.b2 23100b2 $$[0, -1, 0, -1068908, 425718312]$$ $$33766427105425744/9823275$$ $$39293100000000$$ $$$$ $$248832$$ $$1.9748$$
23100.b3 23100b1 $$[0, -1, 0, -66533, 6725562]$$ $$-130287139815424/2250652635$$ $$-562663158750000$$ $$$$ $$124416$$ $$1.6283$$ $$\Gamma_0(N)$$-optimal
23100.b4 23100b3 $$[0, -1, 0, 257467, 32038062]$$ $$7549996227362816/6152409907875$$ $$-1538102476968750000$$ $$$$ $$373248$$ $$2.1776$$

## Rank

sage: E.rank()

The elliptic curves in class 23100.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 23100.b do not have complex multiplication.

## Modular form 23100.2.a.b

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} - q^{11} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 