Properties

 Label 930.d Number of curves $2$ Conductor $930$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("930.d1")

sage: E.isogeny_class()

Elliptic curves in class 930.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
930.d1 930d2 [1, 1, 0, -37442, 2585844] [2] 5376
930.d2 930d1 [1, 1, 0, 2238, 181236] [2] 2688 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Modular form930.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} - 4q^{13} - 2q^{14} - q^{15} + q^{16} - 6q^{17} - q^{18} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.