Properties

 Label 98736bw Number of curves $2$ Conductor $98736$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

Elliptic curves in class 98736bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
98736.bv2 98736bw1 [0, -1, 0, -23272, 1115248] [2] 276480 $$\Gamma_0(N)$$-optimal
98736.bv1 98736bw2 [0, -1, 0, -352392, 80630640] [2] 552960

Rank

sage: E.rank()

The elliptic curves in class 98736bw have rank $$1$$.

Complex multiplication

The elliptic curves in class 98736bw do not have complex multiplication.

Modular form 98736.2.a.bw

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - 2q^{7} + q^{9} - 4q^{13} - 2q^{15} - q^{17} + 2q^{19} + O(q^{20})$$

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 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.