# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2310.d1")

sage: E.isogeny_class()

## Elliptic curves in class 2310d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.d3 2310d1 [1, 1, 0, -77, -291]  512 $$\Gamma_0(N)$$-optimal
2310.d2 2310d2 [1, 1, 0, -157, 301] [2, 2] 1024
2310.d1 2310d3 [1, 1, 0, -2137, 37129]  2048
2310.d4 2310d4 [1, 1, 0, 543, 2961]  2048

## Rank

sage: E.rank()

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

## Modular form2310.2.a.d

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 