Properties

 Label 930h Number of curves $2$ Conductor $930$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

Elliptic curves in class 930h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
930.h2 930h1 $$[1, 0, 1, 467, -1432]$$ $$11298232190519/7472736000$$ $$-7472736000$$ $$$$ $$960$$ $$0.58334$$ $$\Gamma_0(N)$$-optimal
930.h1 930h2 $$[1, 0, 1, -2013, -12344]$$ $$901456690969801/457629750000$$ $$457629750000$$ $$$$ $$1920$$ $$0.92991$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form930.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} - 4 q^{13} + 2 q^{14} + q^{15} + q^{16} + 2 q^{17} - q^{18} - 8 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels. 