# Properties

 Label 2310.v Number of curves 4 Conductor 2310 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2310.v1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.v1 2310v3 [1, 0, 0, -49280, -4214808] [2] 3072
2310.v2 2310v2 [1, 0, 0, -3080, -66048] [2, 2] 1536
2310.v3 2310v4 [1, 0, 0, -2960, -71400] [2] 3072
2310.v4 2310v1 [1, 0, 0, -200, -960] [4] 768 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form2310.2.a.v

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 LMFDB 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 LMFDB labels.