# Properties

 Label 930.b Number of curves $4$ Conductor $930$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("930.b1")

sage: E.isogeny_class()

## Elliptic curves in class 930.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.b1 930a3 [1, 1, 0, -6628, 204952]  1152
930.b2 930a2 [1, 1, 0, -428, 2832] [2, 2] 576
930.b3 930a1 [1, 1, 0, -108, -432]  288 $$\Gamma_0(N)$$-optimal
930.b4 930a4 [1, 1, 0, 652, 16008]  1152

## Rank

sage: E.rank()

The elliptic curves in class 930.b have rank $$1$$.

## Modular form930.2.a.b

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 