# Properties

 Label 2475.g Number of curves 4 Conductor 2475 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2475.g1")
sage: E.isogeny_class()

## Elliptic curves in class 2475.g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
2475.g1 2475g3 [1, -1, 0, -32967, -2293434] 2 6144
2475.g2 2475g2 [1, -1, 0, -2592, -15309] 4 3072
2475.g3 2475g1 [1, -1, 0, -1467, 21816] 2 1536 $$\Gamma_0(N)$$-optimal
2475.g4 2475g4 [1, -1, 0, 9783, -126684] 2 6144

## Rank

sage: E.rank()

The elliptic curves in class 2475.g have rank $$0$$.

## Modular form2475.2.a.g

sage: E.q_eigenform(10)
$$q + q^{2} - q^{4} - 4q^{7} - 3q^{8} - q^{11} + 2q^{13} - 4q^{14} - q^{16} - 2q^{17} + O(q^{20})$$

## 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. 