# Properties

 Label 52878.g Number of curves 2 Conductor 52878 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("52878.g1")

sage: E.isogeny_class()

## Elliptic curves in class 52878.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52878.g1 52878f2 [1, 0, 0, -1169746, -38244568738] [] 6667920
52878.g2 52878f1 [1, 0, 0, -1127536, 462330752]  952560 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 52878.g have rank $$0$$.

## Modular form 52878.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 