# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2310.c1")

sage: E.isogeny_class()

## Elliptic curves in class 2310.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.c1 2310c3 [1, 1, 0, -12183, 510237]  6144
2310.c2 2310c2 [1, 1, 0, -1183, -2363] [2, 2] 3072
2310.c3 2310c1 [1, 1, 0, -863, -10107]  1536 $$\Gamma_0(N)$$-optimal
2310.c4 2310c4 [1, 1, 0, 4697, -12947]  6144

## Rank

sage: E.rank()

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

## Modular form2310.2.a.c

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 