Properties

 Label 303450s Number of curves $2$ Conductor $303450$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

Elliptic curves in class 303450s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.s2 303450s1 [1, 1, 0, 158800, 56577750] [] 4976640 $$\Gamma_0(N)$$-optimal
303450.s1 303450s2 [1, 1, 0, -1466825, -1765747875] [] 14929920

Rank

sage: E.rank()

The elliptic curves in class 303450s have rank $$0$$.

Complex multiplication

The elliptic curves in class 303450s do not have complex multiplication.

Modular form 303450.2.a.s

sage: E.q_eigenform(10)

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.