# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2310.k1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.k1 2310j4 [1, 0, 1, -266113, 52815788]  12288
2310.k2 2310j3 [1, 0, 1, -18033, 676876]  12288
2310.k3 2310j2 [1, 0, 1, -16633, 824156] [2, 2] 6144
2310.k4 2310j1 [1, 0, 1, -953, 15068]  3072 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form2310.2.a.k

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 