Properties

 Label 9800.bj Number of curves $2$ Conductor $9800$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9800.bj1")

sage: E.isogeny_class()

Elliptic curves in class 9800.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9800.bj1 9800bg2 [0, -1, 0, -49408, 4192812] [2] 30720
9800.bj2 9800bg1 [0, -1, 0, -408, 174812] [2] 15360 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 9800.bj have rank $$1$$.

Modular form9800.2.a.bj

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{9} - 2q^{17} + 2q^{19} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.