# Properties

 Label 4030.a Number of curves 2 Conductor 4030 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4030.a1")
sage: E.isogeny_class()

## Elliptic curves in class 4030.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4030.a1 4030a2 [1, -1, 0, -3304, -72000] 2 3136
4030.a2 4030a1 [1, -1, 0, -104, -2240] 2 1568 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4030.a have rank $$0$$.

## Modular form4030.2.a.a

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 