Properties

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

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("930.o1")

sage: E.isogeny_class()

Elliptic curves in class 930o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.o6 930o1 [1, 0, 0, 60, -1008] [4] 512 $$\Gamma_0(N)$$-optimal
930.o5 930o2 [1, 0, 0, -1220, -15600] [2, 4] 1024
930.o2 930o3 [1, 0, 0, -19220, -1027200] [2, 2] 2048
930.o4 930o4 [1, 0, 0, -3700, 67232] [8] 2048
930.o1 930o5 [1, 0, 0, -307520, -65664060] [2] 4096
930.o3 930o6 [1, 0, 0, -18920, -1060740] [2] 4096

Rank

sage: E.rank()

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

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.