Properties

 Label 2450.q Number of curves $2$ Conductor $2450$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

Elliptic curves in class 2450.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2450.q1 2450j1 [1, -1, 0, -3292, -71884] [] 2880 $$\Gamma_0(N)$$-optimal
2450.q2 2450j2 [1, -1, 0, 22958, 684116] [] 20160

Rank

sage: E.rank()

The elliptic curves in class 2450.q have rank $$0$$.

Complex multiplication

The elliptic curves in class 2450.q do not have complex multiplication.

Modular form2450.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} + 3q^{3} + q^{4} - 3q^{6} - q^{8} + 6q^{9} - 2q^{11} + 3q^{12} + q^{16} - 4q^{17} - 6q^{18} + 6q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.