# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2310.j1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.j1 2310k3 [1, 0, 1, -9538, -358762]  6144
2310.j2 2310k4 [1, 0, 1, -7718, 258806]  6144
2310.j3 2310k2 [1, 0, 1, -788, -1762] [2, 2] 3072
2310.j4 2310k1 [1, 0, 1, 192, -194]  1536 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form2310.2.a.j

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 