# Properties

 Label 6930.h Number of curves 4 Conductor 6930 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.h1")
sage: E.isogeny_class()

## Elliptic curves in class 6930.h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.h1 6930k4 [1, -1, 0, -95040009, 356645502765] 2 491520
6930.h2 6930k3 [1, -1, 0, -6050889, 5354872173] 2 491520
6930.h3 6930k2 [1, -1, 0, -5940009, 5573682765] 4 245760
6930.h4 6930k1 [1, -1, 0, -364329, 90559053] 2 122880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6930.h have rank $$1$$.

## Modular form6930.2.a.h

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 