# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2310.a1")

sage: E.isogeny_class()

## Elliptic curves in class 2310a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.a3 2310a1 [1, 1, 0, -6958, -224588]  3840 $$\Gamma_0(N)$$-optimal
2310.a2 2310a2 [1, 1, 0, -12078, 143028] [2, 2] 7680
2310.a1 2310a3 [1, 1, 0, -152078, 22739028]  15360
2310.a4 2310a4 [1, 1, 0, 46002, 1176852]  15360

## Rank

sage: E.rank()

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

## Modular form2310.2.a.a

sage: E.q_eigenform(10)

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

## 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. 