# Properties

 Label 2310.e Number of curves $2$ Conductor $2310$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.e1 2310e1 $$[1, 0, 1, -169, -724]$$ $$529278808969/88704000$$ $$88704000$$ $$$$ $$960$$ $$0.24613$$ $$\Gamma_0(N)$$-optimal
2310.e2 2310e2 $$[1, 0, 1, 311, -3988]$$ $$3342032927351/8893500000$$ $$-8893500000$$ $$$$ $$1920$$ $$0.59271$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2310.2.a.e

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 