# Properties

 Label 42630dl Number of curves 2 Conductor 42630 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("42630.dh1")

sage: E.isogeny_class()

## Elliptic curves in class 42630dl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42630.dh2 42630dl1 [1, 0, 0, 7790, -325018] [] 178752 $$\Gamma_0(N)$$-optimal
42630.dh1 42630dl2 [1, 0, 0, -2631210, 1642616100]  1251264

## Rank

sage: E.rank()

The elliptic curves in class 42630dl have rank $$0$$.

## Modular form 42630.2.a.dh

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 