Properties

 Label 9702.g Number of curves $2$ Conductor $9702$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

Elliptic curves in class 9702.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9702.g1 9702s2 $$[1, -1, 0, -23134428, 42834024400]$$ $$46546832455691959/748268928$$ $$22012410332850182784$$ $$$$ $$602112$$ $$2.8444$$
9702.g2 9702s1 $$[1, -1, 0, -1401948, 712131664]$$ $$-10358806345399/1445216256$$ $$-42515053153159200768$$ $$$$ $$301056$$ $$2.4978$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 9702.g have rank $$1$$.

Complex multiplication

The elliptic curves in class 9702.g do not have complex multiplication.

Modular form9702.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2 q^{5} - q^{8} + 2 q^{10} - q^{11} + 4 q^{13} + q^{16} - 6 q^{17} + 2 q^{19} + O(q^{20})$$ 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 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. 