# Properties

 Label 2310.b Number of curves $4$ Conductor $2310$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2310.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.b1 2310b3 $$[1, 1, 0, -2990738, 1982276532]$$ $$2958414657792917260183849/12401051653985258880$$ $$12401051653985258880$$ $$$$ $$100352$$ $$2.5184$$
2310.b2 2310b2 $$[1, 1, 0, -280338, -3362508]$$ $$2436531580079063806249/1405478914998681600$$ $$1405478914998681600$$ $$[2, 2]$$ $$50176$$ $$2.1718$$
2310.b3 2310b1 $$[1, 1, 0, -198418, -34016972]$$ $$863913648706111516969/2486234429521920$$ $$2486234429521920$$ $$$$ $$25088$$ $$1.8252$$ $$\Gamma_0(N)$$-optimal
2310.b4 2310b4 $$[1, 1, 0, 1119342, -25477452]$$ $$155099895405729262880471/90047655797243760000$$ $$-90047655797243760000$$ $$$$ $$100352$$ $$2.5184$$

## Rank

sage: E.rank()

The elliptic curves in class 2310.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2310.b do not have complex multiplication.

## Modular form2310.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + 6 q^{13} + q^{14} + q^{15} + q^{16} + 2 q^{17} - q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 