# Properties

 Label 930o Number of curves $6$ Conductor $930$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 930o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.o6 930o1 $$[1, 0, 0, 60, -1008]$$ $$23862997439/457113600$$ $$-457113600$$ $$[4]$$ $$512$$ $$0.34210$$ $$\Gamma_0(N)$$-optimal
930.o5 930o2 $$[1, 0, 0, -1220, -15600]$$ $$200828550012481/12454560000$$ $$12454560000$$ $$[2, 4]$$ $$1024$$ $$0.68868$$
930.o2 930o3 $$[1, 0, 0, -19220, -1027200]$$ $$785209010066844481/3324675600$$ $$3324675600$$ $$[2, 2]$$ $$2048$$ $$1.0353$$
930.o4 930o4 $$[1, 0, 0, -3700, 67232]$$ $$5601911201812801/1271193750000$$ $$1271193750000$$ $$[8]$$ $$2048$$ $$1.0353$$
930.o1 930o5 $$[1, 0, 0, -307520, -65664060]$$ $$3216206300355197383681/57660$$ $$57660$$ $$[2]$$ $$4096$$ $$1.3818$$
930.o3 930o6 $$[1, 0, 0, -18920, -1060740]$$ $$-749011598724977281/51173462246460$$ $$-51173462246460$$ $$[2]$$ $$4096$$ $$1.3818$$

## Rank

sage: E.rank()

The elliptic curves in class 930o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 930o do not have complex multiplication.

## Modular form930.2.a.o

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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.