Properties

 Label 930.i Number of curves $2$ Conductor $930$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("930.i1")

sage: E.isogeny_class()

Elliptic curves in class 930.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.i1 930i2 [1, 0, 1, -523, -4642] [] 360
930.i2 930i1 [1, 0, 1, 2, -22] [3] 120 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Modular form930.2.a.i

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} - 3q^{11} + q^{12} + 2q^{13} + q^{14} + q^{15} + q^{16} - q^{18} + 5q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.