# Properties

 Label 426.c Number of curves 2 Conductor 426 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("426.c1")
sage: E.isogeny_class()

## Elliptic curves in class 426.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
426.c1 426a2 [1, 0, 0, -230, -5202] 1 400
426.c2 426a1 [1, 0, 0, -20, 48] 5 80 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 426.c have rank $$0$$.

## Modular form426.2.a.c

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

## 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.