# Properties

 Label 1254.j Number of curves 2 Conductor 1254 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1254.j1")
sage: E.isogeny_class()

## Elliptic curves in class 1254.j

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1254.j1 1254k2 [1, 0, 0, -12285, -545847] 1 3000
1254.j2 1254k1 [1, 0, 0, 75, 1953] 5 600 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1254.j have rank $$0$$.

## Modular form1254.2.a.j

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

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.