# Properties

 Label 2310.k Number of curves $4$ Conductor $2310$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.k1 2310j4 $$[1, 0, 1, -266113, 52815788]$$ $$2084105208962185000201/31185000$$ $$31185000$$ $$$$ $$12288$$ $$1.4415$$
2310.k2 2310j3 $$[1, 0, 1, -18033, 676876]$$ $$648474704552553481/176469171805080$$ $$176469171805080$$ $$$$ $$12288$$ $$1.4415$$
2310.k3 2310j2 $$[1, 0, 1, -16633, 824156]$$ $$508859562767519881/62240270400$$ $$62240270400$$ $$[2, 2]$$ $$6144$$ $$1.0950$$
2310.k4 2310j1 $$[1, 0, 1, -953, 15068]$$ $$-95575628340361/43812679680$$ $$-43812679680$$ $$$$ $$3072$$ $$0.74838$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2310.k have rank $$1$$.

## Complex multiplication

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

## Modular form2310.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - q^{11} + q^{12} + 2 q^{13} + q^{14} + q^{15} + q^{16} - 2 q^{17} - q^{18} - 8 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 