# Properties

 Label 2304.b Number of curves $4$ Conductor $2304$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 2304.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2304.b1 2304o3 $$[0, 0, 0, -5826, -171160]$$ $$58591911104/243$$ $$90699264$$ $$[2]$$ $$1280$$ $$0.73631$$
2304.b2 2304o4 $$[0, 0, 0, -5736, -176704]$$ $$-873722816/59049$$ $$-1410554953728$$ $$[2]$$ $$2560$$ $$1.0829$$
2304.b3 2304o1 $$[0, 0, 0, -66, 200]$$ $$85184/3$$ $$1119744$$ $$[2]$$ $$256$$ $$-0.068409$$ $$\Gamma_0(N)$$-optimal
2304.b4 2304o2 $$[0, 0, 0, 24, 704]$$ $$64/9$$ $$-214990848$$ $$[2]$$ $$512$$ $$0.27816$$

## Rank

sage: E.rank()

The elliptic curves in class 2304.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 2304.b do not have complex multiplication.

## Modular form2304.2.a.b

sage: E.q_eigenform(10)

$$q - 2 q^{5} - 2 q^{7} + 4 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.